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Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford
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Sears and Zemansky's University Physics with Modern Physics 13th Edition solutions

Author: Hugh D. Young; Roger A. Freedman; A. Lewis Ford
Publisher: Addison-Wesley
ISBN: 9780321696861

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Chapter 3 Problems

Chapter: 3 Problem: 42P

Sears and Zemansky's University Physics with Modern Physics 13
A faulty model rocket moves in the xy-plane (the positive y-direction is vertically upward). The rockets acceleration has components \(a_{x}(t)=\alpha t^{2}\) and \(a_{y}(t)=\beta-\gamma t\), where \(\alpha=2.50\mathrm{\ m}/\mathrm{s}^4,\ \beta=9.00\mathrm{\ m}/\mathrm{s}^2\), and \(\gamma=1.40\mathr

Chapter: 3 Problem: 43P

Sears and Zemansky's University Physics with Modern Physics 13
If \(\vec{r}=b t^{2} \hat{\imath}+c t^{3} \hat{j},\) where b and c are positive constants, when does the velocity vector make an angle of \(45.0^{\circ}\) with the \(x\)- and \(y\)-axes? Equation Transcription:

Chapter: 3 Problem: 44P

Sears and Zemansky's University Physics with Modern Physics 13
CALC The position of a dragonfly that is flying parallel to the ground is given as a function of time by \(\vec{r}=\left[2.90 \mathrm{~m}+\left(0.0900 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2}\right] \hat{\imath}-\left(0.0150 \mathrm{~m} / \mathrm{s}^{3}\right) t^{3} \hat{\jmath}\) (a) At what value

Chapter: 3 Problem: 45P

Sears and Zemansky's University Physics with Modern Physics 13
A small toy airplane is flying in the ????????-plane parallel to the ground. In the time interval \(t=1.00 \mathrm{~s}\), its velocity as a function of time is given by \(\vec{v}=\left(1.20 \mathrm{~m} / \mathrm{s}^{2}\right) t \hat{\imath}+\left[12.0 \mathrm{~m} / \mathrm{s}-\left(2.00 \mathrm{~m}

Chapter: 3 Problem: 46P

Sears and Zemansky's University Physics with Modern Physics 13
CALC A bird flies in the xy-plane with a velocity vector given by \(\vec{v}=\left(\alpha-\beta t^{2}\right) \hat{\imath}+\gamma t \hat{\jmath} .\). With \(\alpha=2.4 \mathrm{~m} / \mathrm{s}, \beta=1.6 \mathrm{~m} / \mathrm{s}^{3}, \text { and } \gamma=4.0 \mathrm{~m} / \mathrm{s}^{2}\). The positi

Chapter: 3 Problem: 47P

Sears and Zemansky's University Physics with Modern Physics 13
CP A test rocket is launched by accelerating it along a \(200.0-\mathrm{m}\) incline at \(1.25 \mathrm{~m} / \mathrm{s}^{2}\) starting from rest at point \(A\) (Fig. P3.47). The incline rises at \(35.0^{\circ}\) above the horizontal, and at the instant the rocket leaves it, its engines turn off and i

Chapter: 3 Problem: 48P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 48P Martian Athletics. In the long jump, an athlete launches herself at an angle above the ground and lands at the same height, trying to travel the greatest horizontal distance. Suppose that on earth she is in the air for time T, reaches a maximum height h, and achieves a horizontal dist

Chapter: 3 Problem: 49P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 49P Dynamite! A demolition crew uses dynamite to blow an old building apart. Debris from the explosion flies off in all directions and is later found at distances as far as 50 m from the explosion. Estimate the maximum peed al which debris was blown outward by the explosion. Describe any as

Chapter: 3 Problem: 50P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 50P BIO Spiraling Up. Birds of prey typically rise upward on thermals. The paths these birds take may be spiral-like. You can model the spiral motion as uniform circular motion combined with a constant upward velocity. Assume that a bird completes a circle of radius 6.00 m every 5.00 s and

Chapter: 3 Problem: 51P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 51P A sly 1.5-kg monkey and a jungle veterinarian with a blow-gun loaded with a tranquilizer dart are 25 m above the ground in trees 70 m apart. Just as the veterinarian shoots horizontally at the monkey, the monkey drops from the tree in a vain attempt to escape being hit. What must the mi

Chapter: 3 Problem: 52P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 52P A movie stuntwoman drops from a helicopter that is 30.0 m above the ground and moving with a constant velocity whose components are 10.0 m/s upward and 15.0 m/s horizontal and toward the south. Ignore air resistance. (a) Where on the ground (relative to the position of the helicopter wh

Chapter: 3 Problem: 53P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 53P In fighting forest fires, airplanes work in support of ground crews by dropping water on the fires. For practice, a pilot drops a canister of red dye, hoping to hit a target on the ground below. If the plane is flying in a horizontal path 90.0 m above the ground and has a speed of 64.0

Chapter: 3 Problem: 54P

Sears and Zemansky's University Physics with Modern Physics 13
A cannon, located 60.0 m from the base of a vertical 25.0-m-tall cliff, shoots a 15-kg shell at \(43.0^{\circ}\) above the horizontal toward the cliff. (a) What must the minimum muzzle velocity be for the shell to clear the top of the cliff? (b) The ground at the top of the cliff is level, with a con

Chapter: 3 Problem: 55P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 54P A cannon, located 60.0 m from the base of a vertical 25.0-m-tall cliff, shoots a 15-kg shell at 43.0o above the horizontal toward the cliff. (a) What must the minimum muzzle velocity be for the shell to clear the top of the cliff? (b) The ground at the top of the cliff is level, with a

Chapter: 3 Problem: 56P

Sears and Zemansky's University Physics with Modern Physics 13
As a ship is approaching the dock at \(45.0 \mathrm{~cm} / \mathrm{s}\), an important piece of landing equipment needs to be thrown to it before it can dock. This equipment is thrown at \(\text { q15.0 } \mathrm{m} / \mathrm{s}\) at \(60.0^{\circ}\) above the horizontal from the top of a tower at the

Chapter: 3 Problem: 57P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 57P CP CALC A toy rocket is launched with an initial velocity of 12.0 m/s in the horizontal direction from the roof of a 30.0-m-tall building. The rockets engine produces a horizontal acceleration of (1.60 m/s3)t, in the same direction as the initial velocity, but in the vertical directio

Chapter: 3 Problem: 58P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 58P An Errand of Mercy. An airplane is dropping bales of hay to cattle stranded in a blizzard on the Great Plains. The pilot releases the bales at 150 m above the level ground when the plane is flying at 75 m/s in a direction 55 above the horizontal. How far in front of the cattle should th

Chapter: 3 Problem: 59P

Sears and Zemansky's University Physics with Modern Physics 13
The Longest Home Run. According to the Guinness Book of World Records, the longest home run ever measured was hit by Roy Dizzy Carlyle in a minor league game. The ball traveled 188 m (618 ft) before landing on the ground outside the ballpark. (a) Assuming the balls initial velocity was in a direc

Chapter: 3 Problem: 60P

Sears and Zemansky's University Physics with Modern Physics 13
A water hose is used to fill a large cylindrical storage tank of diameter D and height 2D. The hose shoots the water at \(45^{\circ}\) above the horizontal from the same level as the base of the tank and is a distance 6D away (Fig. P3.60). For what range of launch speeds \(\left(v_{0}\right)\) will t

Chapter: 3 Problem: 61P

Sears and Zemansky's University Physics with Modern Physics 13
A projectile is being launched from ground level with no air resistance. You want to avoid having it enter a temperature inversion layer in the atmosphere a height h above the ground. (a) What is the maximum launch speed you could give this projectile if you shot it straight up? Express your answer i

Chapter: 3 Problem: 62P

Sears and Zemansky's University Physics with Modern Physics 13
Kicking a Field Goal. In U.S. football, after a touchdown the team has the opportunity to earn one more point by kicking the ball over the bar between the goal posts. The bar is 10.0 ft above the ground, and the ball is kicked from ground level, 36.0 ft horizontally from the bar (Fig. P3.62). Footbal

Chapter: 3 Problem: 63P

Sears and Zemansky's University Physics with Modern Physics 13
A grasshopper leaps into the air from the edge of a vertical cliff, as shown in Fig. P3.63. Use information from the figure to find (a) the initial speed of the grasshopper and (b) the height of the cliff. Equation Transcription: Text Transcription: 6.

Chapter: 3 Problem: 64P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 64P A World Record. In the shot put, a standard track and-field event, a 7.3-kg object (the shot) is thrown by releasing it at approximately 40 over a straight left leg. The world record for distance, set by Randy Barnes in 1990, is 23.11 m. Assuming that Barnes released the shot put at 40.0

Chapter: 3 Problem: 65P

Sears and Zemansky's University Physics with Modern Physics 13
Look Out! A snowball rolls off a barn roof that slopes downward at an angle of \(40^{\circ}\) (Fig. P3.65). The edge of the roof is \(14.0 \mathrm{~m}\) above the ground, and the snowball has a speed of \(7.00 \mathrm{~m} / \mathrm{s}\) as it rolls off the roof. Ignore air resistance. (a) How far fro

Chapter: 3 Problem: 66P

Sears and Zemansky's University Physics with Modern Physics 13
On the Flying Trapeze. A new circus act is called the Texas Tumblers. Lovely Mary Belle swings from a trapeze, projects herself at an angle of and is supposed to be caught by Joe Bob, whose hands are 6.1 m above and 8.2 m horizontally from her launch point (Fig. P3.66). You can ignore air resistance.

Chapter: 3 Problem: 67P

Sears and Zemansky's University Physics with Modern Physics 13
A physics professor did daredevil stunts in his spare time. His last stunt was an attempt to jump across a river on a motorcycle (Fig. P3.67). The takeoff ramp was inclined at \(53.0^{\circ}\), the river was 40.0 m wide, and the far bank was 15.0 m lower than the top of the ramp. The river itself was

Chapter: 3 Problem: 68P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 68P A rock is thrown with a velocity v0, at an angle of ?0 from the horizontal, from the roof of a building of height h. Ignore air resistance. Calculate the speed of the rock just before it strikes the ground, and show that this speed is independent of ?0.

Chapter: 3 Problem: 69P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 69P A 5500-kg cart carrying a vertical rocket launcher moves to the right at a constant speed of 30.0 m/s along a horizontal track. It launches a 45.0-kg rocket vertically upward with an initial speed of 40.0 m/s relative to the cart. (a) How high will the rocket go? (b) Where, relative to

Chapter: 3 Problem: 70P

Sears and Zemansky's University Physics with Modern Physics 13
A 2.7-kg ball is thrown upward with an initial speed of 20.0 m/s from the edge of a 45.0-m-high cliff. At the instant the ball is thrown, a woman starts running away from the base of the cliff with a constant speed of 6.00 m/s. The woman runs in a straight line on level ground. Ignore air resistance

Chapter: 3 Problem: 71P

Sears and Zemansky's University Physics with Modern Physics 13
A 76.0-kg boulder is rolling horizontally at the top of a vertical cliff that is 20 m above the surface of a lake, as shown in Fig. P3.71. The top of the vertical face of a dam is located 100 m from the foot of the cliff, with the top of the dam level with the surface of the water in the lake. A leve

Chapter: 3 Problem: 72P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 72P Tossing Your Lunch. Henrietta is jogging on the side-walk at 3.05 m/s on the way to her physics class. Bruce realizes that she forgot her bag of bagels, so he runs to the window, which is 38.0 m above the street level and directly above the sidewalk, to throw the bag to her. He throws i

Chapter: 3 Problem: 1DQ

Sears and Zemansky's University Physics with Modern Physics 13
Problem 1DQ A simple pendulum (a mass swinging at the end of a string) swings back and forth in a circular arc. What is the direction of the acceleration of the mass when it is at the ends of the swing? At the midpoint? In each case, explain how you obtained your answer.

Chapter: 3 Problem: 1E

Sears and Zemansky's University Physics with Modern Physics 13
A squirrel has x- and y-coordinates (1.1 m, 3.4 m) at time \(t_1\) = 0 and coordinates (5.3 m, - 0.5 m) at time \(t_2\) = 3.0 s. For this time interval, find (a) the components of the average velocity, and (b) the magnitude and direction of the average velocity.

Chapter: 3 Problem: 73P

Sears and Zemansky's University Physics with Modern Physics 13
Two tanks are engaged in a training exercise on level ground. The first tank fires a paint-filled training round with a muzzle speed of 250 m / s at \(10.0^{\circ}\) above the horizontal while advancing toward the second tank with a speed of 15.0 m / s relative to the ground. The second tank is retre

Chapter: 3 Problem: 74P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 74P CP Bang! A student sits atop a platform a distance h above the ground. He throws a large firecracker horizontally with a speed. However, a wind blowing parallel to the ground gives the firecracker a constant horizontal acceleration with magnitude a. As a result, the firecracker reaches

Chapter: 3 Problem: 2DQ

Sears and Zemansky's University Physics with Modern Physics 13
Redraw Fig. 3.11a if \(\vec{a}\) is antiparallel to \(\vec{v}_{1}\). Does the particle move in a straight line? What happens to its speed? Equation Transcription: Text Transcription: Vec a Vec v1

Chapter: 3 Problem: 75P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 75P In a Fourth of July celebration, a firework is launched from ground travel with an initial velocity of 25.0 m/s at 30.0 from the vertical. At its maximum height it explodes in a starburst into many fragments, two of which travel forward initially at 20.0 m/s at 53.0 with respect to t

Chapter: 3 Problem: 2E

Sears and Zemansky's University Physics with Modern Physics 13
Problem 2E A rhinoceros is at the origin of coordinates at time t1 = 0. For the time interval from t1 = 0 to t2 = 12.0 s, the rhinos average velocity has x-component - 3.8 m/s and y-component 4.9 m/s. At time t2 = 12.0 s, (a) what are the x- and y-coordinates of the rhino? (b) How far is the rhino

Chapter: 3 Problem: 76P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 76P When it is 145 m above the ground, a rocket traveling vertical by upward at a constant 8.50 m/s relative to the ground launches a secondary rocket at a speed of 12.0 m/s at an angle of 53.0 above the horizontal, both quantities being measured by an astronaut sitting in the rocket. After

Chapter: 3 Problem: 12DQ

Sears and Zemansky's University Physics with Modern Physics 13
Problem 12DQ In uniform circular motion, the acceleration is perpendicular to the velocity at every instant. Is this true when the motion is not uniformthat is, when the speed is not constant?

Chapter: 3 Problem: 77P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 77P In an action-adventure film, the hero is supposed to throw a grenade from his car. which is going 90.0 km/h, to his enemys car, which is going 110 km/h. The enemys car is 15.8 m in front of the heros when he lets go of the grenade. If the hero throws the grenade so its initial velocity

Chapter: 3 Problem: 78P

Sears and Zemansky's University Physics with Modern Physics 13
A 400.0-m-wide river flows from west to east at \(30.0 \mathrm{~m} / \mathrm{min} \text {. }\). Your boat moves at \(100.0 \mathrm{~m} / \mathrm{min}\) relative to the water no matter which direction you point it. To cross this river, you start from a dock at point A on the south bank. There is a boa

Chapter: 3 Problem: 79P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 79P Cycloid. A particle moves in the xy-plane. Its coordinates are given as functions of time by x(t) = R(?t ? sin ?t) y(t) = R(1 ? cos ?t) Where R and ? are constants. (a) Sketch the trajectory of the particle. (This is the trajectory of a point on the rim of a wheel that is rolling at a c

Chapter: 3 Problem: 80P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 80P A projectile is fired from point A at an angle above the horizontal. At its highest point, after having traveled a horizontal distance D from its launch point it suddenly explodes into two identical fragments that travel horizontally with equal but opposite velocities as measured relati

Chapter: 3 Problem: 3DQ

Sears and Zemansky's University Physics with Modern Physics 13
A projectile moves in a parabolic path without air resistance. Is there any point at which \(\vec{a}\) is parallel to \(\vec{v}\)? Perpendicular to \(\vec{v}\)? Explain. Equation Transcription: Text Transcription: Vec{a} Vec{v} vec{v}

Chapter: 3 Problem: 81P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 81P An airplane pilot sets a compass course due west and maintains an airspeed of 220 km/h. After flying for 0.500 h, she finds herself over a town 120 km west and 20 km south of her starting point. (a) Find the wind velocity (magnitude and direction). (b) If the wind velocity is 40 km/h du

Chapter: 3 Problem: 3E

Sears and Zemansky's University Physics with Modern Physics 13
CALC A web page designer creates an animation in which a dot on a computer screen has a position of \(\vec{r}=\left[4.0 \mathrm{~cm}+\left(2.5 \mathrm{~cm} / \mathrm{s}^{2}\right) t^{2}\right] \hat{\imath}+(5.0 \mathrm{~cm} / \mathrm{s}) t \hat{\jmath}\) (a) Find the magnitude and direction of the d

Chapter: 3 Problem: 82P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 82P Raindrops. When a trains velocity is 12.0 m/s east-ward, raindrops that are falling vertically with respect to the earth make traces that are inclined 30.0o to the vertical on the windows of the train. (a) What is the horizontal component of a drops velocity with respect to the earth? Wit

Chapter: 3 Problem: 83P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 83P In a World Cup soccer match, Juan is running due north toward the goal with a speed of 8.00 m/s relative to the ground. A teammate passes the ball to him. The ball has a speed of 12.0 m/s and is moving in a direction 37.0o east of north, relative to the ground. What are the magnitude an

Chapter: 3 Problem: 4DQ

Sears and Zemansky's University Physics with Modern Physics 13
When a rifle is fired at a distant target, the barrel is not lined up exactly on the target. Why not? Does the angle of correction depend on the distance to the target?

Chapter: 3 Problem: 4E

Sears and Zemansky's University Physics with Modern Physics 13
CALC The position of a squirrel running in a park is given by \(\vec{r}=\left[(0.280 \mathrm{~m} / \mathrm{s}) t+\left(0.360 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2}\right] \hat{\imath}+\left(0.0190 \mathrm{~m} / \mathrm{s}^{3}\right) t^{3} \hat{\jmath} .\) (a) What are \(v_{x}(t) \text { and } v_{

Chapter: 3 Problem: 84P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 84P An elevator is moving upward at a constant speed of 2.50 m/s. A bolt in the elevator ceiling 3.00 m above the elevator floor works loose and falls. (a) How long does it take for the bolt to fall to the elevator floor? What is the speed of the bolt just as it hits the elevator floor (b)

Chapter: 3 Problem: 5DQ

Sears and Zemansky's University Physics with Modern Physics 13
Problem 5DQ At the instant that you fire a bullet horizontally from a rifle, you drop a bullet from the height of the gun barrel. If there is no air resistance, which bullet hits the level ground first? Explain.

Chapter: 3 Problem: 85P

Sears and Zemansky's University Physics with Modern Physics 13
Suppose the elevator in Problem 3.84 starts from rest and maintains a constant upward acceleration of \(4.00\mathrm{\ m}/\mathrm{s}^2\), and the bolt falls out the instant the elevator begins to move. (a) How long does it take for the bolt to reach the floor of the elevator? (b) Just as it reaches th

Chapter: 3 Problem: 5E

Sears and Zemansky's University Physics with Modern Physics 13
Problem 5E A jet plane is flying at a constant altitude. At time t1 = 0, it has components of velocity vx = 90 m/s, vy = 110 m/s. At time t2 = 30.0 s, the components are vx = - 170 m/s, vy = 40 m/s. (a) Sketch the velocity vectors at t1 and t2. How do these two vectors differ? For this time interva

Chapter: 3 Problem: 86P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 86P Two soccer players, Mia and Alice, are running as Alice passes the ball to Mia. Mia is running due north with a speed of 6.00 m/s. The velocity of the ball relative to Mia is 5.00 m/s in a direction 30.0 east of south. What are the magnitude and direction of the velocity of the ball rel

Chapter: 3 Problem: 6DQ

Sears and Zemansky's University Physics with Modern Physics 13
A package falls out of an airplane that is flying in a straight line at a constant altitude and speed. If you ignore air resistance, what would be the path of the package as observed by the pilot? As observed by a person on the ground?

Chapter: 3 Problem: 6E

Sears and Zemansky's University Physics with Modern Physics 13
Problem 6E A dog running in an open field has components of velocity vx = 2.6 m/s and vy = -1.8 m/s at t1 = 10.0 s. For the time interval from t1 = 10.0 s to t2 = 20.0 s, the average acceleration of the dog has magnitude 0.45 m/s2 and direction 31.0o measured from the + x-axis toward the + y-axis.

Chapter: 3 Problem: 7DQ

Sears and Zemansky's University Physics with Modern Physics 13
Problem 7DQ Sketch the six graphs of the x- and y-components of position, velocity, and acceleration versus time for projectile motion with x0 = y0 = 0 and 0 < ?0 < 90o.

Chapter: 3 Problem: 87P

Sears and Zemansky's University Physics with Modern Physics 13
Problem 87P Projectile Motion on an Incline. Refer to the Bridging Problem in chapter 3. (a) An archer on ground that has a constant upward slope of 30.0 aims at a target 60.0 in farther up the incline. The arrow in the bow and the bulls-eye at the center of the target are each 1.50 m above the gr

Chapter: 3 Problem: 7E

Sears and Zemansky's University Physics with Modern Physics 13
Problem 7E CALC The coordinates of a bird flying in the xy-plane are given by x(t) = ?t and y(t) = 3.0 m - ?t2, where ? = 2.4 m/s and ? = 1.2 m/s2. (a) Sketch the path of the bird between t = 0 and t = 2.0 s. (b) Calculate the velocity and acceleration vectors of the bird as functions of time. (c)

Chapter: 3 Problem: 88CP

Sears and Zemansky's University Physics with Modern Physics 13
Problem 88CP CALC A projectile thrown from a point P moves in such a way that its distance from P is always increasing. Find the maximum angle above the horizontal with which the projectile could have been thrown. Ignore air resistance.

Chapter: 3 Problem: 89CP

Sears and Zemansky's University Physics with Modern Physics 13
Problem 89CP Two students are canoeing on a river. While heading upstream, they accidentally drop an empty bottle overboard. They then continue paddling for 60 minutes, reaching a point 2.0 km farther upstream. At this point they realize that the bottle is missing and, driven by ecological awarenes

Chapter: 3 Problem: 8DQ

Sears and Zemansky's University Physics with Modern Physics 13
If a jumping frog can give itself the same initial speed regardless of the direction in which it jumps (forward or straight up), how is the maximum vertical height to which it can jump related to its maximum horizontal range \(R_{\max}=v_0^{\ 2}/g\)?

Chapter: 3 Problem: 8E

Sears and Zemansky's University Physics with Modern Physics 13
A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by \(\vec{v}=\left[5.00 \mathrm{\ m} / \mathrm{s}-\left(0.0180 \mathrm{\ m} / \mathrm{s}^{3}\right) t^{2}\right] \hat{\imath}+\left[2.00 \mathrm{\ m} / \mathrm{s}+\left(0.550 \mathrm{\ m}

Chapter: 3 Problem: 9DQ

Sears and Zemansky's University Physics with Modern Physics 13
Problem 9DQ A projectile is fired upward at an angle ? above the horizontal with an initial speed v0. At its maximum height, what are its velocity vector, its speed, and its acceleration vector?

Chapter: 3 Problem: 9E

Sears and Zemansky's University Physics with Modern Physics 13
A physics book slides off a horizontal tabletop with a speed of 1.10 m/s. It strikes the floor in 0.350 s. Ignore air resistance. Find (a) the height of the tabletop above the floor; (b) the horizontal at distance from the edge of the table to the point where the book strikes the floor; (c) the horiz

Chapter: 3 Problem: 10DQ

Sears and Zemansky's University Physics with Modern Physics 13
Problem 10DQ In uniform circular motion, what are the average velocity and average acceleration for one revolution? Explain.

Chapter: 3 Problem: 10E

Sears and Zemansky's University Physics with Modern Physics 13
A daring 510-N swimmer dives off a cliff with a running horizontal leap, as shown in Fig. E3.10. What must her minimum speed be just as she leaves the top of the cliff so that she will miss the ledge at the bottom, which is \(1.75 \mathrm{~m}\) wide and \(9.00 \mathrm{~m}\) below the top of the cliff

Chapter: 3 Problem: 11DQ

Sears and Zemansky's University Physics with Modern Physics 13
Problem 11DQ In uniform circular motion, how does the acceleration change when the speed is increased by a factor of 3? When the radius is decreased by a factor of 2?

Chapter: 3 Problem: 11E

Sears and Zemansky's University Physics with Modern Physics 13
Problem 11E Two crickets, Chirpy and Milada, jump from the top of a vertical cliff. Chirpy just drops and reaches the ground in 3.50 s, while Milada jumps horizontally with an initial speed of 95.0 cm/s. How far from the base of the cliff will Milada hit the ground?

Chapter: 3 Problem: 12E

Sears and Zemansky's University Physics with Modern Physics 13
Problem 12E A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. (a) How much time is required for the football to reach the highest point of the trajectory? (b) How high is this point? (

Chapter: 3 Problem: 90CP

Sears and Zemansky's University Physics with Modern Physics 13
Problem 90CP CP A rocket designed to place small payloads into orbit is carried to an altitude of 12.0 km above sea level by a converted airliner. When the airliner is flying in a straight line at a constant speed of 850 km/h, the rocket is dropped. After the drop, the air-liner maintains the same

Chapter: 3 Problem: 13DQ

Sears and Zemansky's University Physics with Modern Physics 13
Problem 13DQ Raindrops hitting the side windows of a car in motion often leave diagonal streaks even if there is no wind. Why? Is the explanation the same or different for diagonal streaks on the windshield?

Chapter: 3 Problem: 13E

Sears and Zemansky's University Physics with Modern Physics 13
Leaping the River I. A car traveling on a level horizontal road comes to a bridge during a storm and finds the bridge washed out. The driver must get to the other side, so he decides to try leaping it with his car. The side of the road the car is on is 21.3 m above the river, while the opposite side

Chapter: 3 Problem: 14DQ

Sears and Zemansky's University Physics with Modern Physics 13
In a rainstorm with a strong wind, what determines the best position in which to hold an umbrella?

Chapter: 3 Problem: 14E

Sears and Zemansky's University Physics with Modern Physics 13
Problem 14E BIO The Champion Jumper of the Insect World. The froghopper, Philaenus spumarius, holds the world record for insect jumps. When leaping at an angle of 58.0 above the horizontal, some of the tiny critters have reached a maximum height of 58.7 cm above the level ground. (See Nature, Vol.

Chapter: 3 Problem: 15DQ

Sears and Zemansky's University Physics with Modern Physics 13
Problem 15DQ You are on the west bank of a river that is flowing north with a speed of 1.2 m/s. Your swimming speed relative to the water is 1.5 m/s, and the river is 60 m wide. What is your path relative to the earth that allows you to cross the river in the shortest time? Explain your reasoning.

Chapter: 3 Problem: 15E

Sears and Zemansky's University Physics with Modern Physics 13
Inside a starship at rest on the earth, a ball rolls off the top of a horizontal table and lands a distance D from the foot of the table. This starship now lands on the unexplored Planet X. The commander, Captain Curious, rolls the same ball off the same table with the same initial speed as on earth

Chapter: 3 Problem: 16DQ

Sears and Zemansky's University Physics with Modern Physics 13
A stone is thrown into the air at an angle above the horizontal and feels negligible air resistance. Which graph in Fig. Q3.16 best depicts the stones speed \(v\) as a function of time \(t\) while it is in the air? Equation Transcripti

Chapter: 3 Problem: 16E

Sears and Zemansky's University Physics with Modern Physics 13
On level ground a shell is fired with an initial velocity of 50.0 m/s at \(60.0^{\circ}\) above the horizontal and feels no appreciable air resistance. (a) Find the horizontal and vertical components of the shells initial velocity. (b) How long does it take the shell to reach its highest point? (c) F

Chapter: 3 Problem: 17E

Sears and Zemansky's University Physics with Modern Physics 13
A major leaguer hits a baseball so that it leaves the bat at a speed of 30.0 m/s and at an angle of 36.9 above the horizontal. You can ignore air resistance. (a) At what two times is the baseball at a height of 10.0 m above the point at which it left the bat? (b) Calculate the horizontal and vertical

Chapter: 3 Problem: 18E

Sears and Zemansky's University Physics with Modern Physics 13
A shot putter releases the shot some distance above the level ground with a velocity of \(12.0 \mathrm{~m} / \mathrm{s}, 51.0^{\circ}\)above the horizontal. The shot hits the ground 2.08 s later. You can ignore air resistance. (a) What are the components of the shots acceleration while in flight? (

Chapter: 3 Problem: 19E

Sears and Zemansky's University Physics with Modern Physics 13
Win the Prize. In a carnival booth, you win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of \(2.1 \mathrm{~m}\) from this point (Fig. E3.19). If you toss the coin with a velocity of \(

Chapter: 3 Problem: 20E

Sears and Zemansky's University Physics with Modern Physics 13
Suppose the departure angle \(\text { o } 0\) in Fig. 3.26 is \(42.0^{\circ}\) and the distance d is 3.00 m. Where will the dart and monkey meet if the initial speed of the dart is (a) 12.0 m/s? (b) 8.0 m/s? (c) What will happen if the initial speed of the dart is 4.0 m/s? Sketch the trajectory in ea

Chapter: 3 Problem: 21E

Sears and Zemansky's University Physics with Modern Physics 13
Problem 21E A man stands on the roof of a 15.0-m-tall building and throws a rock with a speed of 30.0 m/s at an angle of 33.0o above the horizontal. Ignore air resistance. Calculate (a) the maximum height above the roof that the rock reaches; (b) the speed of the rock just before it strikes the gro

Chapter: 3 Problem: 22E

Sears and Zemansky's University Physics with Modern Physics 13
Firemen use a high-pressure hose to shoot a stream of water at a burning building. The water has a speed of 25.0 m/s as it leaves the end of the hose and then exhibits projectile motion. The firemen adjust the angle of elevation ? of the hose until the water takes 3.00 s to reach a building 45.0 m aw

Chapter: 3 Problem: 23E

Sears and Zemansky's University Physics with Modern Physics 13
Problem 23E A 124-kg balloon carrying a 22-kg basket is descending with a constant downward velocity of 20.0 m/s. A 1.0-kg stone is thrown from the basket with an initial velocity of 15.0 m/s perpendicular to the path of the descending balloon as measured relative to a person at rest in the basket.

Chapter: 3 Problem: 24E

Sears and Zemansky's University Physics with Modern Physics 13
Dizziness. Our balance is maintained, at least in part, by the endolymph fluid in the inner ear. Spinning displaces this fluid, causing dizziness. Suppose a dancer (or skater) is spinning at a very fast 3.0 revolutions per second about a vertical axis through the center of his head. Although the dist

Chapter: 3 Problem: 25E

Sears and Zemansky's University Physics with Modern Physics 13
The earth has a radius of \(380 \mathrm{~km}\) and turns around once on its axis in \(24 \mathrm{~h}\). (a) What is the radial acceleration of an object at the earth's equator? Give your answer in \(\mathrm{m} / \mathrm{s}^{2}\) and as a fraction of \(g\). (b) If \(a_{\text {rad }}\) at the equator i

Chapter: 3 Problem: 26E

Sears and Zemansky's University Physics with Modern Physics 13
A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. (a) What is the linear speed of the blade tip, in m/s? (b) What is the radial acceleration of the blade tip expressed as a multiple of the acc

Chapter: 3 Problem: 27E

Sears and Zemansky's University Physics with Modern Physics 13
BIO Pilot Blackout in a Power Dive. A jet plane comes in for a downward dive as shown in Fig. E3.27. The bottom part of the path is a quarter circle with a radius of curvature of \(350 \mathrm{~m}\). According to medical tests, pilots lose consciousness at an acceleration of 5.5????. At what speed (

Chapter: 3 Problem: 28E

Sears and Zemansky's University Physics with Modern Physics 13
Problem 28E The radius of the earths orbit around the sun (assumed to be circular) is 1.50 X 108 km, and the earth travels around this orbit in 365 days. (a) What is the magnitude of the orbital velocity of the earth, in m/s? (b) What is the radial acceleration of the earth toward the sun, in m/s2?

Chapter: 3 Problem: 29E

Sears and Zemansky's University Physics with Modern Physics 13
A Ferris wheel with radius 14.0 m is turning about a horizontal axis through its center (Fig. E3.29). The linear speed of a passenger on the rim is constant and equal to 7.00 m/s. What are the magnitude and direction of the passengers acceleration as she passes through (a) the lowest point in he

Chapter: 3 Problem: 30E

Sears and Zemansky's University Physics with Modern Physics 13
Problem 30E BIO Hypergravity. At its Ames Research Center, NASA uses its large 20-G centrifuge to test the effects of very large accelerations (hypergravity) on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and an astronaut is strapped

Chapter: 3 Problem: 31E

Sears and Zemansky's University Physics with Modern Physics 13
A moving sidewalk in an airport terminal building moves at 1.0 m/s and is 35.0 m long. If a woman steps on at one end and walks at 1.5 m/s relative to the moving sidewalk, how much time does she require to reach the opposite end if she walks (a) in the same direction the sidewalk is moving? (b) In th

Chapter: 3 Problem: 32E

Sears and Zemansky's University Physics with Modern Physics 13
A railroad flatcar is traveling to the right at a speed of \(13.0 \mathrm{~m} / \mathrm{s}\) relative to an observer standing on the ground. Someone is riding a motor scooter on the flatcar (Fig. E3.32). What is the velocity (magnitude and direction) of the motor scooter relative to the flatcar if it

Chapter: 3 Problem: 33E

Sears and Zemansky's University Physics with Modern Physics 13
Problem 33E A canoe has a velocity of 0.40 m/s southeast relative to the earth. The canoe is on a river that is flowing 0.50 m/s east relative to the earth. Find the velocity (magnitude and direction) of the canoe relative to the river.

Chapter: 3 Problem: 34E

Sears and Zemansky's University Physics with Modern Physics 13
Two piers, A and B, are located on a river: B is \(1500 \mathrm{~m}\) downstream from A (Fig. E3.34). Two friends must make round trips from pier A to pier B and return. One rows a boat at a constant speed of 4.00 \(\mathrm{~km} / \mathrm{h}\) relative to the water; the other walks on the shore at a

Chapter: 3 Problem: 35E

Sears and Zemansky's University Physics with Modern Physics 13
Crossing the River I. A river flows due south with a speed of 2.0 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4.2 m/s due east. The river is 800 m wide. (a) What is his velocity (magnitude and direction) relative to the earth? (b) How much time is r

Chapter: 3 Problem: 36E

Sears and Zemansky's University Physics with Modern Physics 13
Problem 36E Crossing the River II. (a) In which direction should the motorboat in head in order to reach a point on the opposite bank directly east from the starting point? (The boats speed relative to the water remains 4.2 m/s.) (b) What is the velocity of the boat relative to the earth? (c) How

Chapter: 3 Problem: 37E

Sears and Zemansky's University Physics with Modern Physics 13
The nose of an ultralight plane is pointed south, and its airspeed indicator shows 35 m/s. The plane is in a 10-m/s wind blowing toward the southwest relative to the earth. (a) In a vector addition diagram, show the relationship of \(\vec{v}_{P / E}\) (the velocity of the plane relative to the earth

Chapter: 3 Problem: 38E

Sears and Zemansky's University Physics with Modern Physics 13
An airplane pilot wishes to fly due west. A wind of 80.0 km/h (about 50 mi/h) is blowing toward the south. (a) If the airspeed of the plane (its speed in still air) is 320.0 km/h (about 200 mi/h), in which direction should the pilot head? (b) What is the speed of the plane over the ground? Illustrate

Chapter: 3 Problem: 39E

Sears and Zemansky's University Physics with Modern Physics 13
Bird Migration. Canadian geese migrate essentially along a northsouth direction for well over a thousand kilometers in some cases, traveling at speeds up to about 100 km/h. If one such bird is flying at 100 km/h relative to the air, but there is a 40 km/h wind blowing from west to east, (a) at what a

Chapter: 3 Problem: 40P

Sears and Zemansky's University Physics with Modern Physics 13
An athlete starts at point A and runs at a constant speed of 6.0 m/s around a circular track 100 m in diameter, as shown in Fig. P3.40. Find the \(x \text { and } y \text {-components }\) of this runners average velocity and average acceleration between points (a) A and B, (b) A and C, (c) C and D, a

Chapter: 3 Problem: 3.1

Sears and Zemansky's University Physics with Modern Physics 13
A squirrel has x- and y-coordinates at time and coordinates at time For this time interval, find (a) the components of the average velocity, and (b) the magnitude and direction of the average velocity.

Chapter: 3 Problem: 3.2

Sears and Zemansky's University Physics with Modern Physics 13
A rhinoceros is at the origin of coordinates at time For the time interval from to the rhinos average velocity has x-component and y-component At time (a) what are the x- and y-coordinates of the rhino? (b) How far is the rhino from the origin?

Chapter: 3 Problem: 3.3

Sears and Zemansky's University Physics with Modern Physics 13
CALC A web page designer creates an animation in which a dot on a computer screen has a position of (a) Find the magnitude and direction of the dots average velocity between and (b) Find the magnitude and direction of the instantaneous velocity at and (c) Sketch the dots trajectory from to and show

Chapter: 3 Problem: 3.4

Sears and Zemansky's University Physics with Modern Physics 13
CALC The position of a squirrel running in a park is given by . (a) What are and , the x- and y-components of the velocity of the squirrel, as functions of time? (b) At , how far is the squirrel from its initial position? (c) At what are the magnitude and direction of the squirrels velocity?

Chapter: 3 Problem: 3.5

Sears and Zemansky's University Physics with Modern Physics 13
A jet plane is flying at a constant altitude. At time it has components of velocity At time the components are (a) Sketch the velocity vectors at and How do these two vectors differ? For this time interval calculate (b) the components of the average acceleration, and (c) the magnitude and direction o

Chapter: 3 Problem: 3.6

Sears and Zemansky's University Physics with Modern Physics 13
A dog running in an open field has components of velocity and at For the time interval from to the average acceleration of the dog has magnitude and direction measured from the toward the At (a) what are the x- and y-components of the dogs velocity? (b) What are the magnitude and direction of the do

Chapter: 3 Problem: 3.7

Sears and Zemansky's University Physics with Modern Physics 13
The coordinates of a bird flying in the xy-plane are given by \(x(t)=\alpha t\) and \(y(t)=3.0\mathrm{\ m}-\beta t^2\) where \(\alpha=2.4\mathrm{\ m}/\mathrm{s}\) and \(\beta=1.2\mathrm{\ m}/\mathrm{s}^2\). Sketch the path of the bird between t = 0 and t = 2.0 s. (b) Calculate the velocity and accele

Chapter: 3 Problem: 3.8

Sears and Zemansky's University Physics with Modern Physics 13
CALC A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by (a) What are and , the x- and y-components of the velocity of the car as functions of time? (b) What are the magnitude and direction of the velocity of the car at ? (b) What are t

Chapter: 3 Problem: 3.9

Sears and Zemansky's University Physics with Modern Physics 13
A physics book slides off a horizontal tabletop with a speed of 1.10 m/s. It strikes the floor in 0.350 s. Ignore air resistance. Find (a) the height of the tabletop above the floor; (b) the horizontal distance from the edge of the table to the point where the book strikes the floor; (c) the horizont

Chapter: 3 Problem: 3.10

Sears and Zemansky's University Physics with Modern Physics 13
A daring 510-N swimmer dives off a cliff with a running horizontal leap, as shown in Fig. E3.10. What must her minimum speed be just as she leaves the top of the cliff so that she will miss the ledge at the bottom, which is 1.75 m wide and 9.00 m below the top of the cliff?

Chapter: 3 Problem: 3.11

Sears and Zemansky's University Physics with Modern Physics 13
Two crickets, Chirpy and Milada, jump from the top of a vertical cliff. Chirpy just drops and reaches the ground in 3.50 s, while Milada jumps horizontally with an initial speed of How far from the base of the cliff will Milada hit the ground?

Chapter: 3 Problem: 3.12

Sears and Zemansky's University Physics with Modern Physics 13
A rookie quarterback throws a football with an initial upward velocity component of and a horizontal velocity component of Ignore air resistance. (a) How much time is required for the football to reach the highest point of the trajectory? (b) How high is this point? (c) How much time (after it is thr

Chapter: 3 Problem: 3.13

Sears and Zemansky's University Physics with Modern Physics 13
Leaping the River I. A car traveling on a level horizontal road comes to a bridge during a storm and finds the bridge washed out. The driver must get to the other side, so he decides to try leaping it with his car. The side of the road the car is on is 21.3 m above the river, while the opposite side

Chapter: 3 Problem: 3.14

Sears and Zemansky's University Physics with Modern Physics 13
BIO The Champion Jumper of the Insect World. The froghopper, Philaenus spumarius, holds the world record for insect jumps. When leaping at an angle of 58.0 above the horizontal, some of the tiny critters have reached a maximum height of 58.7 cm above the level ground. (See Nature, Vol. 424, July 31,

Chapter: 3 Problem: 3.15

Sears and Zemansky's University Physics with Modern Physics 13
Inside a starship at rest on the earth, a ball rolls off the top of a horizontal table and lands a distance D from the foot of the table. This starship now lands on the unexplored Planet X. The commander, Captain Curious, rolls the same ball off the same table with the same initial speed as on earth

Chapter: 3 Problem: 3.16

Sears and Zemansky's University Physics with Modern Physics 13
On level ground a shell is fired with an initial velocity of at 60.0 above the horizontal and feels no appreciable air resistance. (a) Find the horizontal and vertical components of the shells initial velocity. (b) How long does it take the shell to reach its highest point? (c) Find its maximum heigh

Chapter: 3 Problem: 3.17

Sears and Zemansky's University Physics with Modern Physics 13
A major leaguer hits a baseball so that it leaves the bat at a speed of 30.0 m/s and at an angle of \(36.9^{\circ}\) above the horizontal. You can ignore air resistance. (a) At what two times is the baseball at a height of 10.0 m above the point at which it left the bat? (b) Calculate the ho

Chapter: 3 Problem: 3.18

Sears and Zemansky's University Physics with Modern Physics 13
A shot putter releases the shot some distance above the level ground with a velocity of above the horizontal. The shot hits the ground 2.08 s later. You can ignore air resistance. (a) What are the components of the shots acceleration while in flight? (b) What are the components of the shots velocity

Chapter: 3 Problem: 3.19

Sears and Zemansky's University Physics with Modern Physics 13
Win the Prize. In a carnival booth, you win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point (Fig. E3.19). If you toss the coin with a velocity of 6.4 m/s at an an

Chapter: 3 Problem: 3.20

Sears and Zemansky's University Physics with Modern Physics 13
Suppose the departure angle \(\alpha_{0}\) in Fig. 3.26 is \(42.0^{\circ}\) and the distance d is 3.00 m. Where will the dart and monkey meet if the initial speed of the dart is (a) 12.0 m/s? (b) 8.0 m/s? (c) What will happen if the initial speed of the dart is 4.0 m/s? Sketch the trajectory in each

Chapter: 3 Problem: 3.21

Sears and Zemansky's University Physics with Modern Physics 13
A man stands on the roof of a 15.0-m-tall building and throws a rock with a velocity of magnitude at an angle of above the horizontal. You can ignore air resistance. Calculate (a) the maximum height above the roof reached by the rock; (b) the magnitude of the velocity of the rock just before it strik

Chapter: 3 Problem: 3.22

Sears and Zemansky's University Physics with Modern Physics 13
Firemen are shooting a stream of water at a burning building using a high-pressure hose that shoots out the water with a speed of as it leaves the end of the hose. Once it leaves the hose, the water moves in projectile motion. The firemen adjust the angle of elevation of the hose until the water take

Chapter: 3 Problem: 3.23

Sears and Zemansky's University Physics with Modern Physics 13
A 124-kg balloon carrying a 22-kg basket is descending with a constant downward velocity of A 1.0-kg stone is thrown from the basket with an initial velocity of perpendicular to the path of the descending balloon, as measured relative to a person at rest in the basket. The person in the basket sees t

Chapter: 3 Problem: 3.24

Sears and Zemansky's University Physics with Modern Physics 13
BIO Dizziness. Our balance is maintained, at least in part, by the endolymph fluid in the inner ear. Spinning displaces this fluid, causing dizziness. Suppose a dancer (or skater) is spinning at a very fast 3.0 revolutions per second about a vertical axis through the center of his head. Although the

Chapter: 3 Problem: 3.25

Sears and Zemansky's University Physics with Modern Physics 13
The earth has a radius of 6380 km and turns around once on its axis in 24 h. (a) What is the radial acceleration of an object at the earths equator? Give your answer in and as a fraction of g. (b) If at the equator is greater than g, objects will fly off the earths surface and into space. (We will se

Chapter: 3 Problem: 3.26

Sears and Zemansky's University Physics with Modern Physics 13
A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at (a) What is the linear speed of the blade tip, in (b) What is the radial acceleration of the blade tip expressed as a multiple of the acceleration of gravi

Chapter: 3 Problem: 3.27

Sears and Zemansky's University Physics with Modern Physics 13
BIO Pilot Blackout in a Power Dive. A jet plane comes in for a downward dive as shown in Fig. E3.27. The bottom part of the path is a quarter circle with a radius of curvature of 350 m. According to medical tests, pilots lose consciousness at an acceleration of 5.5g. At what speed (in and in mph) wi

Chapter: 3 Problem: 3.28

Sears and Zemansky's University Physics with Modern Physics 13
The radius of the earths orbit around the sun (assumed to be circular) is \(1.50\times 10^8\mathrm{\ km}\) and the earth travels around this orbit in 365 days. (a) What is the magnitude of the orbital velocity of the earth, in m/s? (b) What is the radial acceleration of the earth toward the s

Chapter: 3 Problem: 3.29

Sears and Zemansky's University Physics with Modern Physics 13
A Ferris wheel with radius 14.0 m is turning about a horizontal axis through its center (Fig. E3.29). The linear speed of a passenger on the rim is constant and equal to What are the magnitude and direction of the passengers acceleration as she passes through (a) the lowest point in her circular mot

Chapter: 3 Problem: 3.30

Sears and Zemansky's University Physics with Modern Physics 13
BIO Hypergravity. At its Ames Research Center, NASA uses its large 20-G centrifuge to test the effects of very large accelerations (hypergravity) on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and the astronaut is strapped in at the othe

Chapter: 3 Problem: 3.31

Sears and Zemansky's University Physics with Modern Physics 13
A moving sidewalk in an airport terminal building moves at and is 35.0 m long. If a woman steps on at one end and walks at relative to the moving sidewalk, how much time does she require to reach the opposite end if she walks (a) in the same direction the sidewalk is moving? (b) In the opposite direc

Chapter: 3 Problem: 3.32

Sears and Zemansky's University Physics with Modern Physics 13
A railroad flatcar is traveling to the right at a speed of relative to an observer standing on the ground. Someone is riding a motor scooter on the flatcar (Fig. E3.32). What is the velocity (magnitude and direction) of the motor scooter relative to the flatcar if its velocity relative to the observe

Chapter: 3 Problem: 3.33

Sears and Zemansky's University Physics with Modern Physics 13
A canoe has a velocity of southeast relative to the earth. The canoe is on a river that is flowing east relative to the earth. Find the velocity (magnitude and direction) of the canoe relative to the river.

Chapter: 3 Problem: 3.34

Sears and Zemansky's University Physics with Modern Physics 13
Two piers, A and B, are located on a river: B is 1500 m downstream from A (Fig. E3.34). Two friends must make round trips from pier A to pier B and return. One rows a boat at a constant speed of 4.00 km/h relative to the water; the other walks on the shore at a constant speed of 4.00 km/h. The veloci

Chapter: 3 Problem: 3.35

Sears and Zemansky's University Physics with Modern Physics 13
Crossing the River I. A river flows due south with a speed of 2.0 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4.2 m/s due east. The river is 800 m wide. (a) What is his velocity (magnitude and direction) relative to the earth? (b) How much time is r

Chapter: 3 Problem: 3.36

Sears and Zemansky's University Physics with Modern Physics 13
Crossing the River II. (a) In which direction should the motorboat in Exercise 3.35 head in order to reach a point on the opposite bank directly east from the starting point? (The boats speed relative to the water remains ) (b) What is the velocity of the boat relative to the earth? (c) How much time

Chapter: 3 Problem: 3.37

Sears and Zemansky's University Physics with Modern Physics 13
The nose of an ultralight plane is pointed south, and its airspeed indicator shows 35 m/s. The plane is in a 10-m/s wind blowing toward the southwest relative to the earth. (a) In a vector-addition diagram, show the relationship of \(\vec{\boldsymbol{v}}_{\mathrm{P} / \mathrm{E}}\) (the velocity of t

Chapter: 3 Problem: 3.38

Sears and Zemansky's University Physics with Modern Physics 13
An airplane pilot wishes to fly due west. A wind of 80.0 km/h (about 50 mi/h ) is blowing toward the south. (a) If the airspeed of the plane (its speed in still air) is (about 200 mi/h), in which direction should the pilot head? (b) What is the speed of the plane over the ground? Illustrate

Chapter: 3 Problem: 3.39

Sears and Zemansky's University Physics with Modern Physics 13
Bird Migration. Canadian geese migrate essentially along a north-south direction for well over a thousand kilometers in some cases, traveling at speeds up to about 100 km/h. If one such bird is flying at 100 km/h relative to the air, but there is a 40 km/h wind blowing from west to east, (a) at what

Chapter: 3 Problem: 3.40

Sears and Zemansky's University Physics with Modern Physics 13
An athlete starts at point A and runs at a constant speed of around a circular track 100 m in diameter, as shown in Fig. P3.40. Find the xand y-components of this runners average velocity and average acceleration between points (a) A and B, (b) A and C, (c) C and D, and (d) A and A (a full lap). (e)

Chapter: 3 Problem: 3.41

Sears and Zemansky's University Physics with Modern Physics 13
CALC A rocket is fired at an angle from the top of a tower of height Because of the design of the engines, its position coordinates are of the form and where A, B, C, and D are constants. Furthermore, the acceleration of the rocket 1.00 s after firing is Take the origin of coordinates to be at the b

Chapter: 3 Problem: 3.42

Sears and Zemansky's University Physics with Modern Physics 13
CALC A faulty model rocket moves in the xy-plane (the positive y-direction is vertically upward). The rockets acceleration has components and where and At the rocket is at the origin and has velocity with and (a) Calculate the velocity and position vectors as functions of time. (b) What is the maxim

Chapter: 3 Problem: 3.43

Sears and Zemansky's University Physics with Modern Physics 13
CALC If \(\vec{r}=bt^2\hat{i}+ct^3\hat{j}\) where b and c are positive constants, when does the velocity vector make an angle of 45.0 with the x - and y -axes?

Chapter: 3 Problem: 3.44

Sears and Zemansky's University Physics with Modern Physics 13
A small toy airplane is flying in the xy-plane parallel to the ground. In the time interval to , its velocity as a function of time is given by . At what value of Is the velocity of the plane perpendicular to its acceleration?

Chapter: 3 Problem: 3.45

Sears and Zemansky's University Physics with Modern Physics 13
. CP CALC A small toy airplane is flying in the xy-plane parallel to the ground. In the time interval to , its velocity as a function of time is given by v . At what value of t is the velocity of the plane perpendicular to its acceleration?

Chapter: 3 Problem: 3.46

Sears and Zemansky's University Physics with Modern Physics 13
A bird flies in the xy-plane with a velocity vector given by \(\vec{\boldsymbol{v}}=\left(\alpha-\beta t^{2}\right) \hat{\boldsymbol{\imath}}+\gamma t \hat{\boldsymbol{j}}\), with \(\alpha=2.4\mathrm{\ m}/\mathrm{s},\ \beta=1.6\mathrm{\ m}/\mathrm{s}^3\), and \(\gamma=4.0\mathrm{\ m}/\mathrm{s}^2\).

Chapter: 3 Problem: 3.47

Sears and Zemansky's University Physics with Modern Physics 13
A test rocket is launched by accelerating it along a 200.0-m incline at starting from rest at point A (Fig. P3.47). The incline rises at 35.0 above the horizontal, and at the instant the rocket leaves it, its engines turn off and it is subject only to gravity (air resistance can be ignored). Find (a

Chapter: 3 Problem: 3.48

Sears and Zemansky's University Physics with Modern Physics 13
In the long jump, an athlete launches herself at an angle above the ground and lands at the same height, trying to travel the greatest horizontal distance. Suppose that on earth she is in the air for time T, reaches a maximum height h, and achieves a horizontal distance D. If she jumped in exactly th

Chapter: 3 Problem: 3.49

Sears and Zemansky's University Physics with Modern Physics 13
Dynamite! A demolition crew uses dynamite to blow an old building apart. Debris from the explosion flies off in all directions and is later found at distances as far as 50 m from the explosion. Estimate the maximum speed at which debris was blown outward by the explosion. Describe any assumptions tha

Chapter: 3 Problem: 3.50

Sears and Zemansky's University Physics with Modern Physics 13
BIO Spiraling Up. It is common to see birds of prey rising upward on thermals. The paths they take may be spiral-like. You can model the spiral motion as uniform circular motion combined with a constant upward velocity. Assume a bird completes a circle of radius 6.00 m every 5.00 s and rises vertical

Chapter: 3 Problem: 3.51

Sears and Zemansky's University Physics with Modern Physics 13
A jungle veterinarian with a blow-gun loaded with a tranquilizer dart and a sly 1.5-kg monkey are each 25 m above the ground in trees 70 m apart. Just as the hunter shoots horizontally at the monkey, the monkey drops from the tree in a vain attempt to escape being hit. What must the minimum muzzle ve

Chapter: 3 Problem: 3.52

Sears and Zemansky's University Physics with Modern Physics 13
A movie stuntwoman drops from a helicopter that is 30.0 m above the ground and moving with a constant velocity whose components are 10.0 m/s upward and 15.0 m/s horizontal and toward the south. You can ignore air resistance. (a) Where on the ground (relative to the position of the helicopter when she

Chapter: 3 Problem: 3.53

Sears and Zemansky's University Physics with Modern Physics 13
In fighting forest fires, airplanes work in support of ground crews by dropping water on the fires. A pilot is practicing In fighting forest fires, airplanes work in support of ground crews by dropping water on the fires. A pilot is practicing

Chapter: 3 Problem: 3.54

Sears and Zemansky's University Physics with Modern Physics 13
A cannon, located 60.0 m from the base of a vertical 25.0-m-tall cliff, shoots a 15-kg shell at \(43.0^{\circ}\) above the horizontal toward the cliff. (a) What must the minimum muzzle velocity be for the shell to clear the top of the cliff? (b) The ground at the top of the cliff is level,

Chapter: 3 Problem: 3.55

Sears and Zemansky's University Physics with Modern Physics 13
An airplane is flying with a velocity of 90.0 m/s at an angle of \(23.0^{\circ}\) above the horizontal. When the plane is 114 m directly above a dog that is standing on level ground, a suitcase drops out of the luggage compartment. How far from the dog will the suitcase land? You can ignore air resis

Chapter: 3 Problem: 3.56

Sears and Zemansky's University Physics with Modern Physics 13
As a ship is approaching the dock at 45.0 cm/s, an important piece of landing equipment needs to be thrown to it before it can dock. This equipment is thrown at 15.0 m/s at \(60.0^{\circ}\) above the horizontal from the top of a tower at the edge of the water, 8.75 m above the ship's deck (Fig. P3.56

Chapter: 3 Problem: 3.57

Sears and Zemansky's University Physics with Modern Physics 13
A toy rocket is launched with an initial velocity of 12.0 m s in the horizontal direction from the roof of a 30.0-m-tall building. The rockets engine produces a horizontal acceleration of , in the same direction as the initial velocity, but in the vertical direction the acceleration is g, downward. A

Chapter: 3 Problem: 3.58

Sears and Zemansky's University Physics with Modern Physics 13
An Errand of Mercy. An airplane is dropping bales of hay to cattle stranded in a blizzard on the Great Plains. The pilot releases the bales at 150 m above the level ground when the plane is flying at in a direction 55 above the horizontal. How far in front of the cattle should the pilot release the h

Chapter: 3 Problem: 3.59

Sears and Zemansky's University Physics with Modern Physics 13
The Longest Home Run. According to the Guinness Book of World Records, the longest home run ever measured was hit by Roy Dizzy Carlyle in a minor league game. The ball traveled 188 m (618 ft) before landing on the ground outside the ballpark. (a) Assuming the balls initial velocity was in a direction

Chapter: 3 Problem: 3.60

Sears and Zemansky's University Physics with Modern Physics 13
A water hose is used to fill a large cylindrical storage tank of diameter D and height 2D. The hose shoots the water at 45 above the horizontal from the same level as the base of the tank and is a distance 6D away (Fig. P3.60). For what range of launch speeds will the water enter the tank? Ignore air

Chapter: 3 Problem: 3.61

Sears and Zemansky's University Physics with Modern Physics 13
A projectile is being launched from ground level with no air resistance. You want to avoid having it enter a temperature inversion layer in the atmosphere a height h above the ground. (a) What is the maximum launch speed you could give this projectile if you shot it straight up? Express your ans

Chapter: 3 Problem: 3.62

Sears and Zemansky's University Physics with Modern Physics 13
Kicking a Field Goal. In U.S. football, after a touchdown the team has the opportunity to earn one more point by kicking the ball over the bar between the goal posts. The bar is 10.0 ft above the ground, and the ball is kicked from ground level, 36.0 ft horizontally from the bar (Fig. P3.62). Footbal

Chapter: 3 Problem: 3.63

Sears and Zemansky's University Physics with Modern Physics 13
A grasshopper leaps into the air from the edge of a vertical cliff, as shown in Fig. P3.63. Use information from the figure to find (a) the initial speed of the grasshopper and (b) the height of the cliff.

Chapter: 3 Problem: 3.64

Sears and Zemansky's University Physics with Modern Physics 13
A World Record. In the shot put, a standard trackand-field event, a 7.3-kg object (the shot) is thrown by releasing it at approximately 40 over a straight left leg. The world record for distance, set by Randy Barnes in 1990, is 23.11 m. Assuming that Barnes released the shot put at 40.0 from a height

Chapter: 3 Problem: 3.65

Sears and Zemansky's University Physics with Modern Physics 13
Look Out! A snowball rolls off a barn roof that slopes downward at an angle of (Fig. P3.65). The edge of the roof is 14.0 m above the ground, and the snowball has a speed of as it rolls off the roof. Ignore air resistance. (a) How far from the edge of the barn does the snowball strike the ground if i

Chapter: 3 Problem: 3.66

Sears and Zemansky's University Physics with Modern Physics 13
On the Flying Trapeze. A new circus act is called the Texas Tumblers. Lovely Mary Belle swings from a trapeze, projects herself at an angle of and is supposed to be caught by Joe Bob, whose hands are 6.1 m above and 8.2 m horizontally from her launch point (Fig. P3.66). You can ignore air resistance.

Chapter: 3 Problem: 3.67

Sears and Zemansky's University Physics with Modern Physics 13
Leaping the River II. A physics professor did daredevil stunts in his spare time. His last stunt was an attempt to jump across a river on a motorcycle (Fig. P3.67). The takeoff ramp was inclined at the river was 40.0 m wide, and the far bank was 15.0 m lower than the top of the ramp. The river itself

Chapter: 3 Problem: 3.68

Sears and Zemansky's University Physics with Modern Physics 13
A rock is thrown from the roof of a building with a velocity \(\nu_0\) at an angle of \(\alpha_0\) from the horizontal. The building has height h. You can ignore air resistance. Calculate the magnitude of the velocity of the rock just before it strikes the ground, and show that this speed is independ

Chapter: 3 Problem: 3.69

Sears and Zemansky's University Physics with Modern Physics 13
A 5500-kg cart carrying a vertical rocket launcher moves to the right at a constant speed of along a horizontal track. It launches a 45.0-kg rocket vertically upward with an initial speed of relative to the cart. (a) How high will the rocket go? (b) Where, relative to the cart, will the rocket land?

Chapter: 3 Problem: 3.70

Sears and Zemansky's University Physics with Modern Physics 13
A 2.7-kg ball is thrown upward with an initial speed of 20.0 m/s from the edge of a 45.0-m-high cliff. At the instant the ball is thrown, a woman starts running away from the base of the cliff with a constant speed of 6.00 m/s. The woman runs in a straight line on level ground, and air resistance act

Chapter: 3 Problem: 3.71

Sears and Zemansky's University Physics with Modern Physics 13
A 76.0-kg boulder is rolling horizontally at the top of a vertical cliff that is 20 m above the surface of a lake, as shown in Fig. P3.71. The top of the vertical face of a dam is located 100 m from the foot of the cliff, with the top of the dam level with the surface of the water in the lake. A leve

Chapter: 3 Problem: 3.72

Sears and Zemansky's University Physics with Modern Physics 13
Tossing Your Lunch. Henrietta is going off to her physics class, jogging down the sidewalk at Her husband Bruce suddenly realizes that she left in such a hurry that she forgot her lunch of bagels, so he runs to the window of their apartment, which is 38.0 m above the street level and directly above t

Chapter: 3 Problem: 3.73

Sears and Zemansky's University Physics with Modern Physics 13
Two tanks are engaged in a training exercise on level ground. The first tank fires a paint-filled training round with a muzzle speed of 250 m s at above the horizontal while advancing toward the second tank with a speed of relative to the ground. The second tank is retreating at relative to the groun

Chapter: 3 Problem: 3.74

Sears and Zemansky's University Physics with Modern Physics 13
Bang! A student sits atop a platform a distance h above the ground. He throws a large firecracker horizontally with a speed However, a wind blowing parallel to the ground gives the firecracker a constant horizontal acceleration with magnitude a. This results in the firecracker reaching the ground dir

Chapter: 3 Problem: 3.75

Sears and Zemansky's University Physics with Modern Physics 13
Bang! A student sits atop a platform a distance h above the ground. He throws a large firecracker horizontally with a speed However, a wind blowing parallel to the ground gives the firecracker a constant horizontal acceleration with magnitude a. This results in the firecracker reaching the ground dir

Chapter: 3 Problem: 3.76

Sears and Zemansky's University Physics with Modern Physics 13
When it is 145 m above the ground, a rocket traveling vertically upward at a constant relative to the ground launches a secondary rocket at a speed of at an angle of 53.0 above the horizontal, both quantities being measured by an astronaut sitting in the rocket. After it is launched the secondary roc

Chapter: 3 Problem: 3.77

Sears and Zemansky's University Physics with Modern Physics 13
In an action-adventure film, the hero is supposed to throw a grenade from his car, which is going 90.0 km/h, to his enemys car, which is going 110 km/h. The enemys car is 15.8 m in front of the heros when he lets go of the grenade. If the hero throws the grenade so its initial velocity relative to hi

Chapter: 3 Problem: 3.78

Sears and Zemansky's University Physics with Modern Physics 13
A 400.0-m-wide river flows from west to east at 30.0 m/min. Your boat moves at 100.0 m/min relative to the water no matter which direction you point it. To cross this river, you start from a dock at point A on the south bank. There is a boat landing directly opposite at point B on the north bank, and

Chapter: 3 Problem: 3.79

Sears and Zemansky's University Physics with Modern Physics 13
Cycloid. A particle moves in the xy-plane. Its coordinates are given as functions of time by where R and are constants. (a) Sketch the trajectory of the particle. (This is the trajectory of a point on the rim of a wheel that is rolling at a constant speed on a horizontal surface. The curve traced out

Chapter: 3 Problem: 3.80

Sears and Zemansky's University Physics with Modern Physics 13
A projectile is fired from point A at an angle above the horizontal. At its highest point, after having traveled a horizontal distance D from its launch point, it suddenly explodes into two identical fragments that travel horizontally with equal but opposite velocities as measured relative to the pro

Chapter: 3 Problem: 3.81

Sears and Zemansky's University Physics with Modern Physics 13
An airplane pilot sets a compass course due west and maintains an airspeed of After flying for 0.500 h, she finds herself over a town 120 km west and 20 km south of her starting point. (a) Find the wind velocity (magnitude and direction). (b) If the wind velocity is due south, in what direction shoul

Chapter: 3 Problem: 3.82

Sears and Zemansky's University Physics with Modern Physics 13
Raindrops. When a trains velocity is 12.0 m/s eastward, raindrops that are falling vertically with respect to the earth make traces that are inclined \(30.0^{\circ}\) to the vertical on the windows of the train. (a) What is the horizontal component of a drops velocity with respect to the earth? W

Chapter: 3 Problem: 3.83

Sears and Zemansky's University Physics with Modern Physics 13
In a World Cup soccer match, Juan is running due north toward the goal with a speed of 8.00 m/s relative to the ground. A teammate passes the ball to him. The ball has a speed of 12.0 m/s and is moving in a direction \(37.0^{\circ}\) east of north, relative to the ground. What are the magnitude and d

Chapter: 3 Problem: 3.84

Sears and Zemansky's University Physics with Modern Physics 13
An elevator is moving upward at a constant speed of A bolt in the elevator ceiling 3.00 m above the elevator floor works loose and falls. (a) How long does it take for the bolt to fall to the elevator floor? What is the speed of the bolt just as it hits the elevator floor (b) according to an observer

Chapter: 3 Problem: 3.85

Sears and Zemansky's University Physics with Modern Physics 13
Suppose the elevator in Problem 3.84 starts from rest and maintains a constant upward acceleration of and the bolt falls out the instant the elevator begins to move. (a) How long does it take for the bolt to reach the floor of the elevator? (b) Just as it reaches the floor, how fast is the bolt movin

Chapter: 3 Problem: 3.86

Sears and Zemansky's University Physics with Modern Physics 13
Two soccer players, Mia and Alice, are running as Alice passes the ball to Mia. Mia is running due north with a speed of 6.00 m s. The velocity of the ball relative to Mia is 5.00 m/s in a direction east of south. What are the magnitude and direction of the velocity of the ball relative to the ground

Chapter: 3 Problem: 3.87

Sears and Zemansky's University Physics with Modern Physics 13
Projectile Motion on an Incline. Refer to the Bridging Problem in Chapter 3. (a) An archer on ground that has a constant upward slope of aims at a target 60.0 m farther up the incline. The arrow in the bow and the bulls-eye at the center of the target are each 1.50 m above the ground. The initial vel

Chapter: 3 Problem: 3.88

Sears and Zemansky's University Physics with Modern Physics 13
A projectile is thrown from a point P. It moves in such a way that its distance from P is always increasing. Find the maximum angle above the horizontal with which the projectile could have been thrown. You can ignore air resistance.

Chapter: 3 Problem: 3.89

Sears and Zemansky's University Physics with Modern Physics 13
Two students are canoeing on a river. While heading upstream, they accidentally drop an empty bottle overboard. They then continue paddling for 60 minutes, reaching a point 2.0 km farther upstream. At this point they realize that the bottle is missing and, driven by ecological awareness, they turn ar

Chapter: 3 Problem: 3.90

Sears and Zemansky's University Physics with Modern Physics 13
A rocket designed to place small payloads into orbit is carried to an altitude of 12.0 km above sea level by a converted airliner. When the airliner is flying in a straight line at a constant speed of 850 km/h, the rocket is dropped. After the drop, the airliner maintains the same altitude and speed

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