Solved: Figure P3.60 illustrates the difference in

Suppose two vectors are added. Under what conditions would the sum of the magnitudes of the vectors equal the magnitude of the resultant vector?

What other functions, if any, can be used to fi nd the angle in part (b)?

A second hiker follows the same path the fi rst day, but then walks 15.0 km east on the second day before turning and reaching the rangers tower. Is the second hikers resultant displacement vector the same as the fi rst hikers, or different?

Is the magnitude of the velocity vector at impact greater than, less than, or equal to the magnitude of the initial velocity vector? Why?

Neglecting air friction effects, what path does the package travel as observed by the pilot? Why?

True or False: Because the x-component of the displacement doesnt depend explicitly on g, the horizontal distance traveled doesnt depend on the acceleration of gravity.

What angle u0 produces the longest jump?

True or False: All other things being equal, if the ball is thrown at half the given speed it will travel half as far.

True or False: Neglecting air friction, a projectile with a horizontal acceleration stays in the air longer than a projectile that is freely falling

Describe the motion of the ball as related by an observer on the ground.

If the speed of the boat relative to the water is increased, what happens to the angle?

The speeds in this example are the same as in Example 3.11. Why isnt the angle the same as before?

A catapult launches a large stone at a speed of 45.0 m/s at an angle of 55.0 with the horizontal. What maximum height does the stone reach? (Neglect air friction.) (a) 45.7 m (b) 32.7 m (c) 69.3 m (d) 83.2 m (e) 102 m

A skier leaves the end of a horizontal ski jump at 22.0 m/s and falls 3.20 m before landing. Neglecting friction, how far horizontally does the skier travel in the air before landing? (a) 9.8 m (b) 12.2 m (c) 14.3 m (d) 17.8 m (e) 21.6 m

A cruise ship sails due north at 4.50 m/s while a coast guard patrol boat heads 45.0 north of west at 5.20 m/s. What is the velocity of the cruise ship relative to the patrol boat? (a) vx 3.68 m/s; vy 0.823 m/s (b) vx 3.68 m/s; vy 8.18 m/s (c) vx 3.68 m/s; vy 8.18 m/s (d) vx 3.68 m/s; vy 0.823 m/s (e) vx 3.68 m/s; vy 1.82 m/s 4. A vecto

A vector lying in the xy-plane has components of opposite sign. The vector must lie in which quadrant? (a) the fi rst quadrant (b) the second quadrant (c) the third quadrant (d) the fourth quadrant (e) either the second or the fourth quadrant

. An athlete runs three-fourths of the way around a circular track. Which of the following statements is true? (a) His average speed is greater than the magnitude of his average velocity. (b) The magnitude of his average velocity is greater than his average speed. (c) His average speed is equal to the magnitude of his average velocity. (d) His average speed is the same as the magnitude of his average velocity if his instantaneous speed is constant. (e) None of statements (a) through (d) is true.

A car moving around a circular track with constant speed (a) has zero acceleration, (b) has an acceleration component in the direction of its velocity, (c) has an acceleration directed away from the center of its path, (d) has an acceleration directed toward the center of its path, or (e) has an acceleration with a direction that cannot be determined from the information given.

A NASA astronaut hits a golf ball on the Moon. Which of the following quantities, if any, remain constant as the ball travels through the lunar vacuum? (a) speed (b) acceleration (c) velocity (d) horizontal component of velocity (e) vertical component of velocity

A projectile is launched from Earths surface at a certain initial velocity at an angle above the horizontal, reaching maximum height after time tmax. Another projectile is launched with the same initial velocity and angle from the surface of the Moon, where the acceleration of gravity is one-sixth that of Earth. Neglecting air resistance (on Earth) and variations in the acceleration of gravity with height, how long does it take the projectile on the Moon to reach its maximum height? (a) tmax (b) tmax /6 (c) !6tmax (d) 36tmax (e) 6tmax

A sailor drops a wrench from the top of a sailboats vertical mast while the boat is moving rapidly and steadily straight forward. Where will the wrench hit the deck? (a) ahead of the base of the mast (b) at the base of the mast (c) behind the base of the mast (d) on the windward side of the base of the mast (e) None of choices (a) through (d) is correct.

A baseball is thrown from the outfi eld toward the catcher. When the ball reaches its highest point, which statement is true? (a) Its velocity and its acceleration are both zero. (b) Its velocity is not zero, but its acceleration is zero. (c) Its velocity is perpendicular to its acceleration. (d) Its acceleration depends on the angle at which the ball was thrown. (e) None of statements (a) through (d) is true.

A student throws a heavy red ball horizontally from a balcony of a tall building with an initial speed v0. At the same time, a second student drops a lighter blue ball from the same balcony. Neglecting air resistance, which statement is true? (a) The blue ball reaches the ground fi rst. (b) The balls reach the ground at the same instant. (c) The red ball reaches the ground fi rst. (d) Both balls hit the ground with the same speed. (e) None of statements (a) through (d) is true.

As an apple tree is transported by a truck moving to the right with a constant velocity, one of its apples shakes loose and falls toward the bed of the truck. Of the curves shown in Figure MCQ3.12, (i) which best describes the path followed by the apple as seen by a stationary observer on the ground, who observes the truck moving from his left to his right? (ii) Which best describes the path as seen by an observer sitting in the truck?

Which of the following quantities are vectors? (a) the velocity of a sports car (b) temperature (c) the volume of water in a can (d) the displacement of a tennis player from the backline of the court to the net (e) the height of a building

If B S is added to A S, under what conditions does the resultant vector have a magnitude equal to A  B? Under what conditions is the resultant vector equal to zero?

Under what circumstances would a vector have components that are equal in magnitude?

As a projectile moves in its path, is there any point along the path where the velocity and acceleration vectors are (a) perpendicular to each other? (b) Parallel to each other?

Two vectors have unequal magnitudes. Can their sum be zero? Explain.

. Explain whether the following particles do or do not have an acceleration: (a) a particle moving in a straight line with constant speed and (b) a particle moving around a curve with constant speed.

A ball is projected horizontally from the top of a building. One second later, another ball is projected horizontally from the same point with the same velocity. At what point in the motion will the balls be closest to each other? Will the fi rst ball always be traveling faster than the second? What will be the time difference between them when the balls hit the ground? Can the horizontal projection velocity of the second ball be changed so that the balls arrive at the ground at the same time?

A spacecraft drifts through space at a constant velocity. Suddenly, a gas leak in the side of the spacecraft causes it to constantly accelerate in a direction perpendicular to the initial velocity. The orientation of the spacecraft does not change, so the acceleration remains perpendicular to the original direction of the velocity. What is the shape of the path followed by the spacecraft?

Determine which of the following moving objects obey the equations of projectile motion developed in this chapter. (a) A ball is thrown in an arbitrary direction. (b) A jet airplane crosses the sky with its engines thrusting the plane forward. (c) A rocket leaves the launch pad. (d) A rocket moves through the sky after its engines have failed. (e) A stone is thrown under water.

Two projectiles are thrown with the same initial speed, one at an angle u with respect to the level ground and the other at angle 90 u. Both projectiles strike the ground at the same distance from the projection point. Are both projectiles in the air for the same length of time?

A ball is thrown upward in the air by a passenger on a train that is moving with constant velocity. (a) Describe the path of the ball as seen by the passenger. Describe the path as seen by a stationary observer outside the train. (b) How would these observations change if the train were accelerating along the track?

Vector A S has a magnitude of 29 units and points in the positive y-direction. When vector B S is added to A S , the resultant vector A S 1 B S points in the negative y-direction with a magnitude of 14 units. Find the magnitude and direction of B

Vector A S has a magnitude of 8.00 units and makes an angle of 45.0 with the positive x-axis. Vector B S also has a magnitude of 8.00 units and is directed along the negative x-axis. Using graphical methods, fi nd (a) the vector sum A S 1 B S and (b) the vector difference A S 2 B

Vector A S is 3.00 units in length and points along the positive x-axis. Vector B S is 4.00 units in length and points along the negative y-axis. Use graphical methods to fi nd the magnitude and direction of the vectors (a) A S 1 B S and (b) A S 2 B S .

Each of the displacement vectors A S and B S shown in Figure P3.4 has a magnitude of 3.00 m. Graphically fi nd (a) A S 1 B S , (b) A S 2 B S , (c) B S 2 A S , and (d) A S 2 2B S .

A roller coaster moves 200 ft horizontally and then rises 135 ft at an angle of 30.0 above the horizontal. Next, it travels 135 ft at an angle of 40.0 below the horizontal. Use graphical techniques to fi nd the roller coasters displacement from its starting point to the end of this movement.

An airplane fl ies 200 km due west from city A to city B and then 300 km in the direction of 30.0 north of west from city B to city C. (a) In straight-line distance, how far is city C from city A? (b) Relative to city A, in what direction is city C? (c) Why is the answer only approximately correct?

A plane fl ies from base camp to lake A, a distance of 280 km at a direction of 20.0 north of east. After dropping off supplies, the plane fl ies to lake B, which is 190 km and 30.0 west of north from lake A. Graphically determine the distance and direction from lake B to the base camp.

A jogger runs 100 m due west, then changes direction for the second leg of the run. At the end of the run, she is 175 m away from the starting point at an angle of 15.0 north of west. What were the direction and length of her second displacement? Use graphical techniques.

A man lost in a maze makes three consecutive displacements so that at the end of his travel he is right back where he started. The fi rst displacement is 8.00 m westward, and the second is 13.0 m northward. Use the graphical method to fi nd the magnitude and direction of the third displacement.

The magnitude of vector A S is 35.0 units and points in the direction 325 counterclockwise from the positive x-axis. Calculate the x- and y-components of this vector.

A golfer takes two putts to get his ball into the hole once he is on the green. The fi rst putt displaces the ball 6.00 m east, the second 5.40 m south. What displacement would have been needed to get the ball into the hole on the fi rst putt?

. A fi gure skater glides along a circular path of radius 5.00 m. If she coasts around one half of the circle, fi nd (a) the magnitude of the displacement vector and (b) what distance she skated. (c) What is the magnitude of the displacement if she skates all the way around the circle?

A girl delivering newspapers covers her route by traveling 3.00 blocks west, 4.00 blocks north, and then 6.00 blocks east. (a) What is her resultant displacement? (b) What is the total distance she travels?

A hiker starts at his camp and moves the following distances while exploring his surroundings: 75.0 m north, 2.50  102 m east, 125 m at an angle 30.0 north of east, and 1.50  102 m south. (a) Find his resultant displacement from camp. (Take east as the positive x-direction and north as the positive y-direction.) (b) Would changes in the order in which the hiker makes the given displacements alter his fi nal position? Explain.

A vector has an x-component of 25.0 units and a ycomponent of 40.0 units. Find the magnitude and direction of the vector.

A quarterback takes the ball from the line of scrimmage, runs backwards for 10.0 yards, then runs sideways parallel to the line of scrimmage for 15.0 yards. At this point, he throws a 50.0-yard forward pass straight downfi eld, perpendicular to the line of scrimmage. What is the magnitude of the footballs resultant displacement?

The eye of a hurricane passes over Grand Bahama Island in a direction 60.0 north of west with a speed of 41.0 km/h. Three hours later the course of the hurricane suddenly shifts due north, and its speed slows to 25.0 km/h. How far from Grand Bahama is the hurricane 4.50 h after it passes over the island?

A small map shows Atlanta to be 730 miles in a direction 5 north of east from Dallas. The same map shows that Chicago is 560 miles in a direction 21 west of north from Atlanta. Assume a fl at Earth and use the given information to fi nd the displacement from Dallas to Chicago.

. A commuter airplane starts from an airport and takes the route shown in Figure P3.19. The plane fi rst fl ies to city A, located 175 km away in a direction 30.0 north of east. Next, it fl ies for 150 km 20.0 west of north, to city B. Finally, the plane fl ies 190 km due west, to city C. Find the location of city C relative to the location of the starting point.

The helicopter view in Figure P3.20 shows two people pulling on a stubborn mule. Find (a) the single force that is equivalent to the two forces shown and (b) the force a third person would have to exert on the mule to make the net force equal to zero. The forces are measured in units of newtons (N).

A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are 4.00 m to the north, 2.00 m 45.0 north of east, and 1.00 m at 30.0 west of south. Starting at the same initial point, an expert golfer could make the hole in what single displacement?

One of the fastest recorded pitches in major-league baseball, thrown by Joel Zumaya in 2006, was clocked at 101.0 mi/h (Fig. P3.22). If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically by the time it reached home plate, 60.5 ft away?

A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 18.0 m/s. The cliff is 50.0 m above a fl at, horizontal beach as shown in Figure P3.23 (page 78). (a) What are the coordinates of the initial position of the stone? (b) What are the components of the initial velocity? (c) Write the equations for the x- and y-components of the velocity of the stone with time. (d) Write the equations for the position of the stone with time, using the coordinates in Figure P3.23. (e) How long after being released does the stone strike the beach below the cliff? (f) With what speed and angle of impact does the stone land?

A peregrine falcon (Fig. P3.24) is the fastest bird, fl ying at a speed of 200 mi/h. Nature has adapted the bird to reach such a speed by placing baffl es in its nose to prevent air from rushing in and slowing it down. Also, the birds eyes adjust their focus faster than the eyes of any other creature, so the falcon can focus quickly on its prey. Assume a peregrine falcon is moving horizontally at its top speed at a height of 100 m above the ground when it brings its wings into its sides and begins to drop in free fall. How far will the bird fall vertically while traveling horizontally a distance of 100 m?

The best leaper in the animal kingdom is the puma, which can jump to a height of 12 ft when leaving the ground at an angle of 45. With what speed, in SI units, must the animal leave the ground to reach that height?

The record distance in the sport of throwing cowpats is 81.1 m. This record toss was set by Steve Urner of the United States in 1981. Assuming the initial launch angle was 45 and neglecting air resistance, determine (a) the initial speed of the projectile and (b) the total time the projectile was in fl ight. (c) Qualitatively, how would the answers change if the launch angle were greater than 45? Explain

. A tennis player standing 12.6 m from the net hits the ball at 3.00 above the horizontal. To clear the net, the ball must rise at least 0.330 m. If the ball just clears the net at the apex of its trajectory, how fast was the ball moving when it left the racket?

From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 8.00 m/s and angle of 20.0 below the horizontal. It strikes the ground 3.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (b) With the positive x-direction chosen to be out the window, fi nd the x- and y-components of the initial velocity. (c) Find the equations for the x- and ycomponents of the position as functions of time. (d) How far horizontally from the base of the building does the ball strike the ground? (e) Find the height from which the ball was thrown. (f) How long does it take the ball to reach a point 10.0 m below the level of launching?

A brick is thrown upward from the top of a building at an angle of 25 to the horizontal and with an initial speed of 15 m/s. If the brick is in fl ight for 3.0 s, how tall is the building?

An artillery shell is fi red with an initial velocity of 300 m/s at 55.0 above the horizontal. To clear an avalanche, it explodes on a mountainside 42.0 s after fi ring. What are the x- and y-coordinates of the shell where it explodes, relative to its fi ring point?

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24.0 below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 4.00 m/s2 for a distance of 50.0 m to the edge of the cliff, which is 30.0 m above the ocean. Find (a) the cars position relative to the base of the cliff when the car lands in the ocean and (b) the length of time the car is in the air.

A fi reman 50.0 m away from a burning building directs a stream of water from a ground-level fi re hose at an angle of 30.0 above the horizontal. If the speed of the stream as it leaves the hose is 40.0 m/s, at what height will the stream of water strike the building?

A projectile is launched with an initial speed of 60.0 m/s at an angle of 30.0 above the horizontal. The projectile lands on a hillside 4.00 s later. Neglect air friction. (a) What is the projectiles velocity at the highest point of its trajectory? (b) What is the straight-line distance from where the projectile was launched to where it hits its target

A soccer player kicks a rock horizontally off a 40.0-m-high cliff into a pool of water. If the player hears the sound of the splash 3.00 s later, what was the initial speed given to the rock? Assume the speed of sound in air to be 343 m/s.

east enters a region where the wind is blowing 1.00  102 mi/h in a direction 30.0 north of east. (a) Find the components of the velocity of the jet airliner relative to the air, v S JA. (b) Find the components of the velocity of the air relative to Earth, v S AE. (c) Write an equation analogous to Equation 3.16 for the velocities v S JA, v S AE, and v S JE. (d) What is the speed and direction of the aircraft relative to the ground?

A boat moves through the water of a river at 10 m/s relative to the water, regardless of the boats direction. If the water in the river is fl owing at 1.5 m/s, how long does it take the boat to make a round trip consisting of a 300-m displacement downstream followed by a 300-m displacement upstream?

A chinook (king) salmon (genus Oncorhynchus) can jump out of water with a speed of 6.26 m/s. (See Problem 4.9, page 111 for an investigation of how the fi sh can leave the water at a higher speed than it can swim underwater.) If the salmon is in a stream with water speed equal to 1.50 m/s, how high in the air can the fi sh jump if it leaves the water traveling vertically upwards relative to the Earth?

. A river fl ows due east at 1.50 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.0 m/s due north relative to the water. (a) What is the velocity of the boat relative to the shore? (b) If the river is 300 m wide, how far downstream has the boat moved by the time it reaches the north shore?

A rowboat crosses a river with a velocity of 3.30 mi/h at an angle 62.5 north of west relative to the water. The river is 0.505 mi wide and carries an eastward current of 1.25 mi/h. How far upstream is the boat when it reaches the opposite shore?

Suppose a chinook salmon needs to jump a waterfall that is 1.50 m high. If the fi sh starts from a distance 1.00 m from the base of the ledge over which the waterfall fl ows, fi nd the x- and y-components of the initial velocity the salmon would need to just reach the ledge at the top of its trajectory. Can the fi sh make this jump? (Remember that a chinook salmon can jump out of the water with a speed of 6.26 m/s.)

A river has a steady speed of 0.500 m/s. A student swims upstream a distance of 1.00 km and swims back to the starting point. (a) If the student can swim at a speed of 1.20 m/s in still water, how long does the trip take? (b) How much time is required in still water for the same length swim? (c) Intuitively, why does the swim take longer when there is a current

A river has a steady speed of vs. A student swims upstream a distance d and back to the starting point. (a) If the student can swim at a speed of v in still water, how much time tup does it take the student to swim upstream a distance d? Express the answer in terms of d, v, and vs. (b) Using the same variables, how much time tdown does it take to swim back downstream to the starting point? (c) Sum the answers found in parts (a) and (b) and show that the time ta required for the whole trip can be written as ta 5 2d/v 1 2 vs 2 /v 2 (d) How much time tb does the trip take in still water? (e) Which is larger, ta or tb? Is it always larger?

A bomber is fl ying horizontally over level terrain at a speed of 275 m/s relative to the ground and at an altitude of 3.00 km. (a) The bombardier releases one bomb. How far does the bomb travel horizontally between its release and its impact on the ground? Ignore the effects of air resistance. (b) Firing from the people on the ground suddenly incapacitates the bombardier before he can call, Bombs away! Consequently, the pilot maintains the planes original course, altitude, and speed through a storm of fl ak. Where is the plane relative to the bombs point of impact when the bomb hits the ground? (c) The plane has a telescopic bombsight set so that the bomb hits the target seen in the sight at the moment of release. At what angle from the vertical was the bombsight set?

A moving walkway at an airport has a speed v1 and a length L. A woman stands on the walkway as it moves from one end to the other, while a man in a hurry to reach his fl ight walks on the walkway with a speed of v2 relative to the moving walkway. (a) How long does it take the woman to travel the distance L? (b) How long does it take the man to travel this distance?

How long does it take an automobile traveling in the left lane of a highway at 60.0 km/h to overtake (become even with) another car that is traveling in the right lane at 40.0 km/h when the cars front bumpers are initially 100 m apart?

You can use any coordinate system you like to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity v S at an angle u with respect to the horizontal. Let the building be 50.0 m tall, the initial horizontal velocity be 9.00 m/s, and the initial vertical velocity be 12.0 m/s. Choose your coordinates such that the positive y-axis is upward, the x-axis is to the right, and the origin is at the point where the ball is released. (a) With these choices, fi nd the balls maximum height above the ground and the time it takes to reach the maximum height. (b) Repeat your calculations choosing the origin at the base of the building.

A Nordic jumper goes off a ski jump at an angle of 10.0 below the horizontal, traveling 108 m horizontally and 55.0 m vertically before landing. (a) Ignoring friction and aerodynamic effects, calculate the speed needed by the skier on leaving the ramp. (b) Olympic Nordic jumpers can make such jumps with a jump speed of 23.0 m/s, which is considerably less than the answer found in part (a). Explain how that is possible.

In a local diner, a customer slides an empty coffee cup down the counter for a refi ll. The cup slides off the counter and strikes the fl oor at distance d from the base of the counter. If the height of the counter is h, (a) fi nd an expression for the time t it takes the cup to fall to the fl oor in terms of the variables h and g. (b) With what speed does the mug leave the counter? Answer in terms of the variables d, g, and h. (c) In the same terms, what is the speed of the cup immediately before it hits the fl oor? (d) In terms of h and d, what is the direction of the cups velocity immediately before it hits the fl oor?

Towns A and B in Figure P3.49 are 80.0 km apart. A couple arranges to drive from town A and meet a couple driving from town B at the lake, L. The two couples leave simultaneously and drive for 2.50 h in the directions shown. Car 1 has a speed of 90.0 km/h. If the cars arrive simultaneously at the lake, what is the speed of car 2?

A chinook salmon has a maximum underwater speed of 3.58 m/s, but it can jump out of water with a speed of 6.26 m/s. To move upstream past a waterfall, the salmon does not need to jump to the top of the fall, but only to a point in the fall where the water speed is less than 3.58 m/s; it can then swim up the fall for the remaining distance. Because the salmon must make forward progress in the water, lets assume it can swim to the top if the water speed is 3.00 m/s. If water has a speed of 1.50 m/s as it passes over a ledge, how far below the ledge will the water be moving with a speed of 3.00 m/s? (Note that water undergoes projectile motion once it leaves the ledge.) If the salmon is able to jump vertically upward from the base of the fall, what is the maximum height of waterfall that the salmon can clear?

A rocket is launched at an angle of 53.0 above the horizontal with an initial speed of 100 m/s. The rocket moves for 3.00 s along its initial line of motion with an acceleration of 30.0 m/s2. At this time, its engines fail and the rocket proceeds to move as a projectile. Find (a) the maximum altitude reached by the rocket, (b) its total time of fl ight, and (c) its horizontal range.

Two canoeists in identical canoes exert the same effort paddling and hence maintain the same speed relative to the water. One paddles directly upstream (and moves upstream), whereas the other paddles directly downstream. With downstream as the positive direction, an observer on shore determines the velocities of the two canoes to be 1.2 m/s and 2.9 m/s, respectively. (a) What is the speed of the water relative to the shore? (b) What is the speed of each canoe relative to the water?

If a person can jump a maximum horizontal distance (by using a 45 projection angle) of 3.0 m on Earth, what would be his maximum range on the Moon, where the free-fall acceleration is g/6 and g 9.80 m/s2? Repeat for Mars, where the acceleration due to gravity is 0.38g.

A daredevil decides to jump a canyon. Its walls are equally high and 10 m apart. He takes off by driving a motorcycle up a short ramp sloped at an angle of 15. What minimum speed must he have in order to clear the canyon?

A home run is hit in such a way that the baseball just clears a wall 21 m high, located 130 m from home plate. The ball is hit at an angle of 35 to the horizontal, and air resistance is negligible. Find (a) the initial speed of the ball, (b) the time it takes the ball to reach the wall, and (c) the velocity components and the speed of the ball when it reaches the wall. (Assume the ball is hit at a height of 1.0 m above the ground.)

A ball is thrown straight upward and returns to the throwers hand after 3.00 s in the air. A second ball is thrown at an angle of 30.0 with the horizontal. At what speed must the second ball be thrown so that it reaches the same height as the one thrown vertically?

A quarterback throws a football toward a receiver with an initial speed of 20 m/s at an angle of 30 above the horizontal. At that instant the receiver is 20 m from the quarterback. In what direction and with what constant speed should the receiver run in order to catch the football at the level at which it was thrown?

A 2.00-m-tall basketball player is standing on the fl oor 10.0 m from the basket, as in Figure P3.58. If he shoots the ball at a 40.0 angle with the horizontal, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The

In a very popular lecture demonstration, a projectile is fi red at a falling target as in Figure P3.59. The projectile leaves the gun at the same instant the target is dropped from rest. Assuming the gun is initially aimed at the target, show that the projectile will hit the target. (One restriction of this experiment is that the projectile must reach the target before the target strikes the fl oor.)

Figure P3.60 illustrates the difference in proportions between the male (m) and female (f) anatomies. The displacements d S 1m and d S 1f from the bottom of the feet to the navel have magnitudes of 104 cm and 84.0 cm, respectively. The displacements d S 2m and d S 2f have magnitudes of 50.0 cm and 43.0 cm, respectively. (a) Find the vector sum of the displacements d S d1 and d S d2 in each case. (b) The male fi gure is 180 cm tall, the female 168 cm. Normalize the displacements of each fi gure to a common height of 200 cm and re-form the vector sums as in part (a). Then fi nd the vector difference between the two sums.

By throwing a ball at an angle of 45, a girl can throw the ball a maximum horizontal distance R on a level fi eld. How far can she throw the same ball vertically upward? Assume her muscles give the ball the same speed in each case. (Is this assumption valid?)

The equation of a parabola is y ax2  bx  c, where a, b, and c are constants. The x- and y-coordinates of a projectile launched from the origin as a function of time are given by x v0xt and y 5 v0yt 2 1 2gt 2 , where v0x and v0y are the components of the initial velocity. (a) Eliminate t from these two equations and show that the path of aprojectile is a parabola and has the form y ax  bx2. (b) What are the values of a, b, and c for the projectile?

A hunter wishes to cross a river that is 1.5 km wide and fl ows with a speed of 5.0 km/h parallel to its banks. The hunter uses a small powerboat that moves at a maximum speed of 12 km/h with respect to the water. What is the minimum time necessary for crossing?

When baseball outfi elders throw the ball, they usually allow it to take one bounce, on the theory that the ball arrives at its target sooner that way. Suppose that, after the bounce, the ball rebounds at the same angle u that it had when it was released (as in Fig. P3.64), but loses half its speed. (a) Assuming that the ball is always thrown with the same initial speed, at what angle u should the ball be thrown in order to go the same distance D with one bounce as a ball thrown upward at 45.0 with no bounce? (b) Determine the ratio of the times for the one-bounce and no-bounce throws.

A daredevil is shot out of a cannon at 45.0 to the horizontal with an initial speed of 25.0 m/s. A net is positioned a horizontal distance of 50.0 m from the cannon. At what height above the cannon should the net be placed in order to catch the daredevil?

Chinook salmon are able to move upstream faster by jumping out of the water periodically; this behavior is called porpoising. Suppose a salmon swimming in still water jumps out of the water with a speed of 6.26 m/s at an angle of 45, sails through the air a distance L before returning to the water, and then swims a distance L underwater at a speed of 3.58 m/s before beginning another porpoising maneuver. Determine the average speed of the fi sh.

A student decides to measure the muzzle velocity of a pellet shot from his gun. He points the gun horizontally. He places a target on a vertical wall a distance x away from the gun. The pellet hits the target a vertical distance y below the gun. (a) Show that the position of the pellet when traveling through the air is given by y Ax2, where A is a constant. (b) Express the constant A in terms of the initial (muzzle) velocity and the free-fall acceleration. (c) If x 3.00 m and y 0.210 m, what is the initial speed of the pellet? 68

A sailboat is heading directly north at a speed of 20 knots (1 knot 0.514 m/s). The wind is blowing towards the east with a speed of 17 knots. Determine the magnitude and direction of the wind velocity as measured on the boat. What is the component of the wind velocity in the direction parallel to the motion of the boat? (See Problem 4.58 for an explanation of how a sailboat can move into the wind.)

. A golf ball with an initial speed of 50.0 m/s lands exactly 240 m downrange on a level course. (a) Neglecting air friction, what two projection angles would achieve this result? (b) What is the maximum height reached by the ball, using the two angles determined in part (a)?

A landscape architect is planning an artifi cial waterfall in a city park. Water fl owing at 0.750 m/s leaves the end of a horizontal channel at the top of a vertical wall 2.35 m high and falls into a pool. (a) How far from the wall will the water land? Will the space behind the waterfall be wide enough for a pedestrian walkway? (b) To sell her plan to the city council, the architect wants to build a model to standard scale, one-twelfth actual size. How fast should the water flow in the channel in the model?

. One strategy in a snowball fi ght is to throw a snowball at a high angle over level ground. Then, while your opponent is watching that snowball, you throw a second one at a low angle timed to arrive before or at the same time as the fi rst one. Assume both snowballs are thrown with a speed of 25.0 m/s. The fi rst is thrown at an angle of 70.0 with respect to the horizontal. (a) At what angle should the second snowball be thrown to arrive at the same point as the fi rst? (b) How many seconds later should the second snowball be thrown after the fi rst in order for both to arrive at the same time?

A dart gun is fi red while being held horizontally at a height of 1.00 m above ground level and while it is at rest relative to the ground. The dart from the gun travels a horizontal distance of 5.00 m. A college student holds the same gun in a horizontal position while sliding down a 45.0 incline at a constant speed of 2.00 m/s. How far will the dart travel if the student fi res the gun when it is 1.00 m above the ground?

The determined Wile E. Coyote is out once more to try to capture the elusive roadrunner. The coyote wears a new pair of Acme power roller skates, which provide a constant horizontal acceleration of 15 m/s2, as shown in Figure P3.73. The coyote starts off at rest 70 m from the edge of a cliff at the instant the roadrunner zips by in the direction of the cliff. (a) If the roadrunner moves with constant speed, fi nd the minimum speed the roadrunner must have to reach the cliff before the coyote. (b) If the cliff is 100 m above the base of a canyon, fi nd where the coyote lands in the canyon. (Assume his skates are still in operation when he is in fl ight and that his horizontal component of acceleration remains constant at 15 m/s2.)