Solved: Calculate the displacement and velocity at times

Problem 1P What must your car's average speed be in order to travel 235 km in 2.75 h?

(I) A bird can fly 25 km/h. How long does it take to fly 3.5 km?

Problem 1CQ Problem Give an example in which there are clear distinctions among distance traveled, displacement, and magnitude of displacement. Specifically identify each quantity in your example.

Problem 1PE Problem Find the following for path A in Figure 2.59: (a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish.

Problem 2CQ Problem Under what circumstances does distance traveled equal magnitude of displacement? What is the only case in which magnitude of displacement and displacement are exactly the same?

Problem 2PE Problem Find the following for path B in Figure 2.59: (a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish.

Problem 3CQ Problem Bacteria move back and forth by using their flagella (structures that look like little tails). Speeds of up to 50 ?m/s (50×10?6 m/s) have been observed. The total distance traveled by a bacterium is large for its size, while its displacement is small. Why is this?

Problem 3P (I) If you are driving 95 km/h along a straight road and you look to the side for 2.0 s. how far do you travel during this inattentive period?

Substitute for and for . Problem 3PE Problem Find the following for path C in Figure 2.59: (a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish. .

Problem 3Q When an object moves with constant velocity, does its average velocity during any time interval differ from its instantaneous velocity at any instant? Explain.

Problem 4CQ Problem A student writes, “A bird that is diving for prey has a speed of ? 10 m /s .” What is wrong with the student’s statement? What has the student actually described? Explain.

Problem 4PE Problem Find the following for path D in Figure 2.59: (a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish

Problem 5CQ Problem What is the speed of the bird in Exercise 2.4? Exercise 2.4: A student writes, “A bird that is diving for prey has a speed of ? 10 m /s .” What is wrong with the student’s statement? What has the student actually described? Explain.

Problem 5PE Problem (a) Calculate Earth’s average speed relative to the Sun. (b) What is its average velocity over a period of one year?

Problem 5P (I) A rolling ball moves from x1= 8.4 cm to x2= -4.2cm during the time from t1 = 3.0 s to t2 = 6.1 s. What is its average velocity over this time interval?

Problem 5Q If one object has a greater speed than a second object, does the first necessarily have a greater acceleration? Explain, using examples.

Problem 6CQ Problem Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain.

Helicopter blade spins at exactly 100 revolutions per minute. Its tip is 5.00 m from the center of rotation. (a) Calculate the average speed of the blade tip in the helicopter’s frame of reference. (b) What is its average velocity over one revolution?

Compare the acceleration of a motorcycle that accelerates from 80 km/h to 90 km/h with the acceleration of a bicycle that accelerates from rest to 10 km/h in the same time.

Problem 7CQ Problem A weather forecast states that the temperature is predicted to be ?5ºCthe following day. Is this temperature a vector or a scalar quantity? Explain.

Problem 7PE Problem The North American and European continents are moving apart at a rate of about 3 cm/y. At this rate how long will it take them to drift 500 km farther apart than they are at present?

Problem 8CQ Problem Give an example (but not one from the text) of a device used to measure time and identify what change in that device indicates a change in time.

Problem 7Q Can an object have a northward velocity and a southward acceleration? Explain

Problem 8PE Problem Land west of the San Andreas fault in southern California is moving at an average velocity of about 6 cm/y northwest relative to land east of the fault. Los Angeles is west of the fault and may thus someday be at the same latitude as San Francisco, which is east of the fault. How far in the future will this occur if the displacement to be made is 590 km northwest, assuming the motion remains constant?

Problem 9CQ Proble m There is a distinction between average speed and the magnitude of average velocity. Give an example that illustrates the difference between these two quantities.

Give an example where both the velocity and acceleration are negative.

Problem 10CQ Problem Does a car’s odometer measure position or displacement? Does its speedometer measure speed or velocity? .

Problem 10PE Problem Tidal friction is slowing the rotation of the Earth. As a result, the orbit of the Moon is increasing in radius at a rate of approximately 4 cm/year. Assuming this to be a constant rate, how many years will pass before the radius of the Moon’s orbit increases by 3.84×106 m (1%)?

Problem 10Q Two cars emerge side by side from a tunnel. Car A is traveling with a speed of 60 km/h and has an acceleration of 40 km/h/ min Car B has a speed of 40 km/h and has an acceleration of 60 km/h /min. Which car is passing the other as they come out of the tunnel? Explain your reasoning.

Problem 11CQ Problem If you divide the total distance traveled on a car trip (as determined by the odometer) by the time for the trip, are you calculating the average speed or the magnitude of the average velocity? Under what circumstances are these two quantities the same?

Problem 11Q Can an object be increasing in speed as its acceleration decreases? If so. give an example. If not. Explain.

Problem 12CQ Problem How are instantaneous velocity and instantaneous speed related to one another? How do they differ?

Problem 12P (II) A car traveling 95 km/h is 210 m behind a truck traveling 75 km /How long will it take the car to reach the truck?

Speed of propagation of the action potential (an electrical signal) in a nerve cell depends (inversely) on the diameter of the axon (nerve fiber). If the nerve cell connecting the spinal cord to your feet is 1.1 m long, and the nerve impulse speed is 18 m/s, how long does it take for the nerve signal to travel this distance?

Problem 13CQ Problem Is it possible for speed to be constant while acceleration is not zero? Give an example of such a situation.

A baseball player hits a ball straight up into the air. It leaves the bat with a speed of 120 km/h. In the absence of air resistance, how fast would the ball be traveling when it is caught at the same height above the ground as it left the bat? Explain.

Problem 13PE Problem Conversations with astronauts on the lunar surface were characterized by a kind of echo in which the earthbound person’s voice was so loud in the astronaut’s space helmet that it was picked up by the astronaut’s microphone and transmitted back to Earth. It is reasonable to assume that the echo time equals the time necessary for the radio wave to travel from the Earth to the Moon and back (that is, neglecting any time delays in the electronic equipment). Calculate the distance from Earth to the Moon given that the echo time was 2.56 s and that radio waves travel at the speed of light (3.00×108 m/s) .

Problem 14CQ Problem Is it possible for velocity to be constant while acceleration is not zero? Explain.

Problem 14P (II) Calculate the average speed and average velocity of a complete round trip in which the outgoing 250 km is covered at 95 km/h. followed by a 1.0-h lunch break, and the return 250 km is covered at 55 km/h.

An example in which velocity is zero yet acceleration is not

Problem 15Q You travel from point A to point B in a car moving at a constant speed of 70km/h Then you travel the same distance from point B to another point C. moving at a constant speed of 90 km/h Is your average speed for the entire trip from A to C equal to 80 km/? Explain why or why not.

Problem 16CQ Problem If a subway train is moving to the left (has a negative velocity) and then comes to a stop, what is the direction of its acceleration? Is the acceleration positive or negative?

Problem 16PE Problem A cheetah can accelerate from rest to a speed of 30.0 m/s in 7.00 s. What is its acceleration?

Problem 17CQ Problem Plus and minus signs are used in one-dimensional motion to indicate direction. What is the sign of an acceleration that reduces the magnitude of a negative velocity? Of a positive velocity?

Problem 17Q Which of these motions is not at constant acceleration: a rock falling from a cliff, an elevator moving from the second floor to the fifth floor making stops along the way, a dish resting on a table? Explain your answers.

Problem 18CQ Problem What information do you need in order to choose which equation or equations to use to solve a problem? Explain.

Problem 18PE Problem A commuter backs her car out of her garage with an acceleration of 1.40 m/s2 . (a) How long does it take her to reach a speed of 2.00 m/s? (b) If she then brakes to a stop in 0.800 s, what is her deceleration?

That an intercontinental ballistic missile goes from rest to a suborbital speed of 6.50 km/s in 60.0 s (the actual speed and time are classified). What is its average acceleration in \(\mathrm{m/s^2}\) and in multiples of g \((9.80~\mathrm{ m/s^2)}\)?

Problem 19CQ Problem What is the last thing you should do when solving a problem? Explain.

Problem 19Q Can an object have zero velocity and nonzero acceleration at the same time? Give examples.

Problem 20CQ Problem What is the acceleration of a rock thrown straight upward on the way up? At the top of its flight? On the way down?

Problem 20PE Problem An Olympic-class sprinter starts a race with an acceleration of 4.50 m/s2 . (a) What is her speed 2.40 s later? (b) Sketch a graph of her position vs. time for this period.

Problem 20Q Can an object have zero acceleration and nonzero velocity at the same time? Give examples.

Problem 21CQ Problem An object that is thrown straight up falls back to Earth. This is one- dimensional motion. (a) When is its velocity zero? (b) Does its velocity change direction? (c) Does the acceleration due to gravity have the same sign on the way up as on the way down?

Problem 21PE Problem A well-thrown ball is caught in a well-padded mitt. If the deceleration of the ball is 2.10×104 m/s2 , and 1.85 ms (1 ms = 10?3 s) elapses from the time the ball first touches the mitt until it stops, what was the initial velocity of the ball?

Problem 22CQ Problem Suppose you throw a rock nearly straight up at a coconut in a palm tree, and the rock misses on the way up but hits the coconut on the way down. Neglecting air resistance, how does the speed of the rock when it hits the coconut on the way down compare with what it would have been if it had hit the coconut on the way up? Is it more likely to dislodge the coconut on the way up or down? Explain.

Problem 22PE Problem A bullet in a gun is accelerated from the firing chamber to the end of the barrel at an average rate of 6.20×105 m/s2 for 8.10×10?4 s . What is its muzzle velocity (that is, its final velocity)?

Problem 23CQ Problem If an object is thrown straight up and air resistance is negligible, then its speed when it returns to the starting point is the same as when it was released. If air resistance were not negligible, how would its speed upon return compare with its initial speed? How would the maximum height to which it rises be affected?

Problem 24CQ Problem The severity of a fall depends on your speed when you strike the ground. All factors but the acceleration due to gravity being the same, how many times higher could a safe fall on the Moon be than on Earth (gravitational acceleration on the Moon is about 1/6 that of the Earth)?

Problem 25CQ Problem How many times higher could an astronaut jump on the Moon than on Earth if his takeoff speed is the same in both locations (gravitational acceleration on the Moon is about 1/6 of g on Earth)?

Problem (a) Explain how you can use the graph of position versus time in Figure 2.54 to describe the change in velocity over time. Identify (b) the time ( ta , tb , tc , td , or te ) at which the instantaneous velocity is greatest, (c) the time at which it is zero, and (d) the time at which it is negative.

Problem 26PE Problem Professional Application: Blood is accelerated from rest to 30.0 cm/s in a distance of 1.80 cm by the left ventricle of the heart. (a) Make a sketch of the situation. (b) List the knowns in this problem. (c) How long does the acceleration take? To solve this part, first identify the unknown, and then discuss how you chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, checking your units. (d) Is the answer reasonable when compared with the time for a heartbeat?

Problem 28CQ Problem (a) Explain how you can determine the acceleration over time from a velocity versus time graph such as the one in Figure 2.56. (b) Based on the graph, how does acceleration change over time?

Problem 27PE Problem In a slap shot, a hockey player accelerates the puck from a velocity of 8.00 m/s to 40.0 m/s in the same direction. If this shot takes 3.33×10?2 s , calculate the distance over which the puck accelerates.

Problem 28PE A powerful motorcycle can accelerate from rest to 26.8 m/ s (100 km/h) in only 3.90 s. (a) What is its average acceleration? (b) How far does it travel in that time?

Problem 29PE Freight trains can produce only relatively small accelerations and decelerations. (a) What is the final velocity of a freight train that accelerates at a rate of 0.0500 m/s2 for 8.00 min, starting with an initial velocity of 4.00 m/s? (b) If the train can slow down at a rate of 0.550 m/s2 , how long will it take to come to a stop from this velocity? (c) How far will it travel in each case?

Problem 29CQ (a) Sketch a graph of acceleration versus time corresponding to the graph of velocity versus time given in Figure 2.57. (b) Identify the time or tim ? es ( ?ta , ? ? tb , t? c , etc.) at which the acceleration is greatest. (c) At which times is it zero? (d) At which times is it negative?

Problem 30CQ Consider the velocity vs. time graph of a person in an elevator shown in Figure 2.58. Suppose the elevator is initially at rest. It then accelerates for 3 seconds, maintains that velocity for 15 seconds, then decelerates for 5 seconds until it stops. The acceleration for the entire trip is not constant so we cannot use the equations of motion from Motion Equations for Constant Acceleration in One Dimension for the complete trip. (We could, however, use them in the three individual sections where acceleration is a constant.) Sketch graphs of (a) position vs. time and (b) acceleration vs. time for this trip.

Problem 30PE A fireworks shell is accelerated from rest to a velocity of 65.0 m/s over a distance of 0.250 m. (a) How long did the acceleration last? (b) Calculate the acceleration.

Problem 31CQ A cylinder is given a push and then rolls up an inclined plane. If the origin is the starting point, sketch the position, velocity, and acceleration of the cylinder vs. time as it goes up and then down the plane.

Problem 31PE A swan on a lake gets airborne by flapping its wings and running on top of the water. (a) If the swan must reach a velocity of 6.00 m/s to take off and it accelerates from rest at an average rate of 0.350 m/s2 , how far will it travel before becoming airborne? (b) How long does this take?

Problem 32PE Professional Application: A woodpecker’s brain is specially protected from large decelerations by tendon-like attachments inside the skull. While pecking on a tree, the woodpecker’s head comes to a stop from an initial velocity of 0.600 m/s in a distance of only 2.00 mm. (a) Find the acceleration in m/s2 and in multiples of ? ? g(?g = 9.80 m/s2). (b) Calculate the stopping time. (c) The tendons cradling the brain stretch, making its stopping distance 4.50 mm (greater than the head and, hence, less deceleration of the brain). What is the brain’s deceleration, expressed in ?multiples of? g ?

Problem 33PE An unwary football player collides with a padded goalpost while running at a velocity of 7.50 m/s and comes to a full stop after compressing the padding and his body 0.350 m. (a) What is his deceleration? (b) How long does the collision last?

Problem 34PE In World War II, there were several reported cases of airmen who jumped from their flaming airplanes with no parachute to escape certain death. Some fell about 20,000 feet (6000 m), and some of them survived, with few lifethreatening injuries. For these lucky pilots, the tree branches and snow drifts on the ground allowed their deceleration to be relatively small. If we assume that a pilot’s speed upon impact was 123 mph (54 m/s), then what was his deceleration? Assume that the trees and snow stopped him over a distance of 3.0 m.

Problem 35PE Consider a grey squirrel falling out of a tree to the ground. (a) If we ignore air resistance in this case (only for the sake of this problem), determine a squirrel’s velocity just before hitting the ground, assuming it fell from a height of 3.0 m. (b) If the squirrel stops in a distance of 2.0 cm through bending its limbs, compare its deceleration with that of the airman in the previous problem.

Problem 36PE An express train passes through a station. It enters with an initial velocity of 22.0 m/s and decelerates at a rate of 0.150 m/s2 as it goes through. The station is 210 m long. (a) How long is the nose of the train in the station? (b) How fast is it going when the nose leaves the station? (c) If the train is 130 m long, when does the end of the train leave the station? (d) What is the velocity of the end of the train as it leaves?

Problem 37PE Dragsters can actually reach a top speed of 145 m/s in only 4.45 s—considerably less time than given in Example 2.10 and Example 2.11. (a) Calculate the average acceleration for such a dragster. (b) Find the final velocity of this dragster starting from rest and accelerating at the rate found in (a) for 402 m (a quarter mile) without using any information on time. (c) Why is the final velocity greater than that used to find the average acceleration? Hint: Consider whether the assumption of constant acceleration is valid for a dragster. If not, discuss whether the acceleration would be greater at the beginning or end of the run and what effect that would have on the final velocity. Example 2.10: Calculating Displacement of an Accelerating Object: Dragsters Dragsters can achieve average accelerations of 26.0 m/s2 . Suppose such a dragster accelerates from rest at this rate for 5.56 s. How far does it travel in this time? Example 2.11: Calculating Final Velocity: Dragsters Calculate the final velocity of the dragster in Example 2.10 without using information about time.

Problem 38PE A bicycle racer sprints at the end of a race to clinch a victory. The racer has an initial velocity of 11.5 m/s and accelerates at the rate of 0.500 m/s2 for 7.00 s. (a) What is his final velocity? (b) The racer continues at this velocity to the finish line. If he was 300 m from the finish line when he started to accelerate, how much time did he save? (c) One other racer was 5.00 m ahead when the winner started to accelerate, but he was unable to accelerate, and traveled at 11.8 m/s until the finish line. How far ahead of him (in meters and in seconds) did the winner finish?

Problem 39PE In 1967, New Zealander Burt Munro set the world record for an Indian motorcycle, on the Bonneville Salt Flats in Utah, with a maximum speed of 183.58 mi/h. The one-way course was 5.00 mi long. Acceleration rates are often described by the time it takes to reach 60.0 mi/h from rest. If this time was 4.00 s, and Burt accelerated at this rate until he reached his maximum speed, how long did it take Burt to complete the course?

Problem 40PE (a) A world record was set for the men’s 100-m dash in the 2008 Olympic Games in Beijing by Usain Bolt of Jamaica. Bolt “coasted” across the finish line with a time of 9.69 s. If we assume that Bolt accelerated for 3.00 s to reach his maximum speed, and maintained that speed for the rest of the race, calculate his maximum speed and his acceleration. (b) During the same Olympics, Bolt also set the world record in the 200-m dash with a time of 19.30 s. Using the same assumptions as for the 100-m dash, what was his maximum speed for this race?

Problem 41PE Calculate the displacement and velocity at times of (a) 0.500, (b) 1.00, (c) 1.50, and (d) 2.00 s for a ball thrown straight up with an initial velocity of 15.0 m/s. Take the point of release to be y0 = 0 .

Problem 42PE Calculate the displacement and velocity at times of (a) 0.500, (b) 1.00, (c) 1.50, (d) 2.00, and (e) 2.50 s for a rock thrown straight down with an initial velocity of 14.0 m/s from the Verrazano Narrows Bridge in New York City. The roadway of this bridge is 70.0 m above the water.

Problem 44PE A rescue helicopter is hovering over a person whose boat has sunk. One of the rescuers throws a life preserver straight down to the victim with an initial velocity of 1.40 m/s and observes that it takes 1.8 s to reach the water. (a) List the knowns in this problem. (b) How high above the water was the preserver released? Note that the downdraft of the helicopter reduces the effects of air resistance on the falling life preserver, so that an acceleration equal to that of gravity is reasonable.

Problem 43PE A basketball referee tosses the ball straight up for the starting tip-off. At what velocity must a basketball player leave the ground to rise 1.25 m above the floor in an attempt to get the ball?

Problem 45PE A dolphin in an aquatic show jumps straight up out of the water at a velocity of 13.0 m/s. (a) List the knowns in this problem. (b) How high does his body rise above the water? To solve this part, first note that the final velocity is now a known and identify its value. Then identify the unknown, and discuss how you chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, checking units, and discuss whether the answer is reasonable. (c) How long is the dolphin in the air? Neglect any effects due to his size or orientation.

Problem 46PE A swimmer bounces straight up from a diving board and falls feet first into a pool. She starts with a velocity of 4.00 m/ s, and her takeoff point is 1.80 m above the pool. (a) How long are her feet in the air? (b) What is her highest point above the board? (c) What is her velocity when her feet hit the water?

Problem 47PE (a) Calculate the height of a cliff if it takes 2.35 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.00 m/s. (b) How long would it take to reach the ground if it is thrown straight down with the same speed?

Problem 48PE A very strong, but inept, shot putter puts the shot straight up vertically with an initial velocity of 11.0 m/s. How long does he have to get out of the way if the shot was released at a height of 2.20 m, and he is 1.80 m tall?

Problem 49PE You throw a ball straight up with an initial velocity of 15.0 m/s. It passes a tree branch on the way up at a height of 7.00 m. How much additional time will pass before the ball passes the tree branch on the way back down?

Problem 51PE Standing at the base of one of the cliffs of Mt. Arapiles in Victoria, Australia, a hiker hears a rock break loose from a height of 105 m. He can’t see the rock right away but then does, 1.50 s later. (a) How far above the hiker is the rock when he can see it? (b) How much time does he have to move before the rock hits his head?

Problem 53PE There is a 250-m-high cliff at Half Dome in Yosemite National Park in California. Suppose a boulder breaks loose from the top of this cliff. (a) How fast will it be going when it strikes the ground? (b) Assuming a reaction time of 0.300 s, how long will a tourist at the bottom have to get out of the way after hearing the sound of the rock breaking loose (neglecting the height of the tourist, which would become negligible anyway if hit)? The speed of sound is 335 m/s on this day.

(II) A certain type of automobile can accelerate approximately as shown in the velocity-time graph of Fig. 2-35. (The short flat spots in the curve represent shifting of the gears.) (a) Estimate the average acceleration of the car in second gear and in fourth gear. (b) Estimate how far the car traveled while in fourth gear. FIGURE 2-35 Problems 52 and 53. The velocity of an automobile as a function of time, starting from a dead stop. The jumps in the curve represent gear shifts.

Problem 54PE A ball is thrown straight up. It passes a 2.00-m-high window 7.50 m off the ground on its path up and takes 1.30 s to go past the window. What was the ball’s initial velocity?

Problem 55PE Suppose you drop a rock into a dark well and, using precision equipment, you measure the time for the sound of a splash to return. (a) Neglecting the time required for sound to travel up the well, calculate the distance to the water if the sound returns in 2.0000 s. (b) Now calculate the distance taking into account the time for sound to travel up the well. The speed of sound is 332.00 m/s in this well.

Problem 56PE A steel ball is dropped onto a hard floor from a height of 1.50 m and rebounds to a height of 1.45 m. (a) Calculate its velocity just before it strikes the floor. (b) Calculate its velocity just after it leaves the floor on its way back up. (c) Calculate its acceleration during contact with the floor if that contact lasts 0.0800 ms (8.00×10?5 s) . (d) How much did the ball compress during its collision with the floor, assuming the floor is absolutely rigid?

Problem 57PE A coin is dropped from a hot-air balloon that is 300 m above the ground and rising at 10.0 m/s upward. For the coin, find (a) the maximum height reached, (b) its position and velocity 4.00 s after being released, and (c) the time before it hits the ground.

The acceleration due to gravity on the Moon is about one sixth what it is on Earth. If an object is thrown vertically upward on the Moon, how many times higher will it go than it would on Earth, assuming the same initial velocity?

Problem 58PE A soft tennis ball is dropped onto a hard floor from a height of 1.50 m and rebounds to a height of 1.10 m. (a) Calculate its velocity just before it strikes the floor. (b) Calculate its velocity just after it leaves the floor on its way back up. (c) Calculate its acceleration during contact with the floor if that contact lasts 3.50 ms (3.50×10?3 s). (d) How much did the ball compress during its collision with the floor, assuming the floor is absolutely rigid?

Problem 59PE (a) By taking the slope of the curve in Figure 2.60, verify that the velocity of the jet car is 115 m/s at t = 20 s . (b) By taking the slope of the curve at any point in Figure 2.61, verify that the jet car’s acceleration is 5.0 m/s2

Problem 60PE Using approximate values, calculate the slope of the curve in Figure 2.62 to verify that the velocity at t = 10.0 s is 0.208 m/s. Assume all values are known to 3 significant figures.

Problem 61PE Using approximate values, calculate the slope of the curve in Figure 2.62 to verify that the velocity at t = 30.0 s is 0.238 m/s. Assume all values are known to 3 significant figures.

Problem 62PE By taking the slope of the curve in Figure 2.63, verify that the acceleration is 3.2 m/s2 at t = 10 s.

Problem 64PE (a) Take the slope of the curve in Figure 2.64 to find the jogger’s velocity at t = 2.5 s . (b) Repeat at 7.5 s. These values must be consistent with the graph in Figure 2.65.

Problem 63PE Construct the displacement graph for the subway shuttle train as shown in Figure 2.18(a). Your graph should show the position of the train, in kilometers, from t = 0 to 20 s. You will need to use the information on acceleration and velocity given in the examples for this figure. Figure 2.18(a):

Problem 65PE A grap?h? of? (?t) is shown for a world-class track sprinter in a 100-m race. (See Figure 2.67). (a) What is his average velocity for the first 4 s? (b) What is his instantaneous velo ? city a? = 5 s ? (c) What is his average acceleration between 0 and 4 s? (d) What is his time for the race?

Problem 66PE Figure 2.68 shows the displacement graph for a particle for 5 s. Draw the corresponding velocity and acceleration graphs.

Problem 17PE Problem Professional Application Dr. John Paul Stapp was U.S. Air Force officer who studied the effects of extreme deceleration on the human body. On December 10, 1954, Stapp rode a rocket sled, accelerating from rest to a top speed of 282 m/s (1015 km/h) in 5.00 s, and was brought jarringly back to rest in only 1.40 s! Calculate his (a) acceleration and (b) deceleration. Express each in multiples of g (9.80 m/s2 ) by taking its ratio to the acceleration of gravity.

Problem 9PE Problem On May 26, 1934, a streamlined, stainless steel diesel train called the Zephyr set the world’s nonstop long-distance speed record for trains. Its run from Denver to Chicago took 13 hours, 4 minutes, 58 seconds, and was witnessed by more than a million people along the route. The total distance traveled was 1633.8 km. What was its average speed in km/h and m/s?

Problem 11PE Problem A student drove to the university from her home and noted that the odometer reading of her car increased by 12.0 km. The trip took 18.0 min. (a) What was her average speed? (b) If the straight-line distance from her home to the university is 10.3 km in a direction 25.0º south of east, what was her average velocity? (c) If she returned home by the same path 7 h 30 min after she left, what were her average speed and velocity for the entire trip?

Problem 14PE Problem A football quarterback runs 15.0 m straight down the playing field in 2.50 s. He is then hit and pushed 3.00 m straight backward in 1.75 s. He breaks the tackle and runs straight forward another 21.0 m in 5.20 s. Calculate his average velocity (a) for each of the three intervals and (b) for the entire motion.

Problem 15PE Problem The planetary model of the atom pictures electrons orbiting the atomic nucleus much as planets orbit the Sun. In this model you can view hydrogen, the simplest atom, as having a single electron in a circular orbit 1.06×10?10 m in diameter. (a) If the average speed of the electron in this orbit is known to be 2.20×106 m/s , calculate the number of revolutions per second it makes about the nucleus. (b) What is the electron’s average velocity?

Describe in words the motion plotted in Fig. in terms of , etc. [Hint: First try to duplicate the motion plotted by walking or moving your hand.]

Problem 24PE Problem While entering a freeway, a car accelerates from rest at a rate of 2.40 m/s2 for 12.0 s. (a) Draw a sketch of the situation. (b) List the knowns in this problem. (c) How far does the car travel in those 12.0 s? To solve this part, first identify the unknown, and then discuss how you chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, check your units, and discuss whether the answer is reasonable. (d) What is the car’s final velocity? Solve for this unknown in the same manner as in part (c), showing all steps explicitly.

Problem 25PE Problem At the end of a race, a runner decelerates from a velocity of 9.00 m/s at a rate of 2.00 m/s2 . (a) How far does she travel in the next 5.00 s? (b) What is her final velocity? (c) Evaluate the result. Does it make sense?

Problem 27CQ Problem (a) Sketch a graph of velocity versus time corresponding to the graph of displacement versus time given in Figure 2.55. (b) Identify the time or times ( ta , tb , tc , etc.) at which the instantaneous velocity is greatest. (c) At which times is it zero? (d) At which times is it negative?

(II) For an object falling freely from rest, show that the distance traveled during each successive second increases in the ratio of successive odd integers , etc. This was first shown by Galileo. See Figs. and .

Figure shows the position vs. time graph for two bicycles, and . Is there any instant at which the two bicycles have the same velocity? Which bicycle has the larger acceleration? (c) At which instant(s) are the bicycles passing each other? Which bicycle is passing the other? Which bicycle has the highest instantaneous velocity? (e) Which bicycle has the higher average velocity?

Does a car speedometer measure speed, velocity, or both?

Problem 2Q Can an object have varying speed if its velocity is constant? If yes, give examples.

Problem 4P Convert 35 mi/h to (a) km/h, (b) m/s, and (c) ft/s.

Problem 4Q In drag racing, is it possible for the car with the greatest speed crossing the finish line to lose the race? Explain.

Problem 6P A particle at t1 = -2.0 s is at x1 = 3.4 cm and at t2 = 4.5 s is at x2 = 8.5 cm. What is its average velocity? Can you calculate its average speed from these data?

(II) You are driving home from school steadily at 95 km/h for 130 km. It then begins to rain and you slow to 65 km/h. You arrive home after driving 3 hours and 20 minutes. (a) How far is your hometown from school? (b) What was your average speed?

(II) According to a rule-of-thumb, every five seconds between a lightning flash and the following thunder gives the distance to the flash in miles. Assuming that the flash of light arrives in essentially no time at all, estimate the speed of sound in \(\mathrm{m} / \mathrm{s}\) from this rule.

Can the velocity of an object be negative when its acceleration is positive? What about vice versa?

Problem 9P A person jogs eight complete laps around a quarter-mile track in a total time of 12.5 min. Calculate (a) the average speed and (b) the average velocity, in m/s.

(II) A horse canters away from its trainer in a straight line, moving 116 m away in 14.0 s. It then turns abruptly and gallops halfway back in 4.8 s. Calculate (a) its average speed and (b) its average velocity for the entire trip, using “away from the trainer” as the positive direction.

Two locomotives approach each other on parallel tracks. Each has a speed of 95 km/h with respect to the ground. If they are initially 8.5 km apart, how long will it be before they reach each other? (See Fig. 2–30).

An airplane travels 3100 km at a speed of 790 km/h, and then encounters a tailwind that boosts its speed to 990 km/h for the next 2800 km. What was the total time for the trip? What was the average speed of the plane for this trip? [Hint: Think carefully before using Eq. 2-11d.]

As a freely falling object speeds up, what is happening to its acceleration due to gravity—does it increase, decrease, or stay the same?

Problem 14Q How would you estimate the maximum height you could throw a ball vertically upward? How would you estimate the maximum speed you could give it?

(III) A bowling ball traveling with constant speed hits the pins at the end of a bowling lane 16.5 m long. The bowler hears the sound of the ball hitting the pins 2.50s after the ball is released from his hands. What is the speed of the ball? The speed of sound is 340 m/s.

(I) A sports car accelerates from rest to \(95 \mathrm{~km} / \mathrm{h}\) in \(6.2 \mathrm{~s}\). What is its average acceleration in \(\mathrm{m} / \mathrm{s}^2\) ?

Problem 16Q In a lecture demonstration, a 3.0-m-long vertical string with ten bolts tied to it at equal intervals is dropped from the ceiling of the lecture hall. The string falls on a tin plate, and the class hears the clink of each bolt as it hits the plate. The sounds will not occur at equal time intervals. Why? Will the time between clinks increase or decrease near the end of the fall? How could the bolts be tied so that the clinks occur at equal intervals?

Problem 17P A sprinter accelerates from rest to 10.0 m/s in 1.35 s. What is her acceleration (a) in m/s2, and (b) in km/h2?

(II) At highway speeds, a particular automobile is capable of an acceleration of about \(1.6 \mathrm{~m} / \mathrm{s}^2\). At this rate, how long does it take to accelerate from \(80 \mathrm{~km} / \mathrm{h}\) to \(110 \mathrm{~km} / \mathrm{h}\)?

An object that is thrown vertically upward will return to its original position with the same speed as it had initially if air resistance is negligible. If air resistance is appreciable, will this result be altered, and if so, how? [Hint: The acceleration due to air resistance is always in a direction opposite to the motion.]

(II) A sports car moving at constant speed travels \(110 \mathrm{~m}\) in \(5.0 \mathrm{~s}\). If it then brakes and comes to a stop in \(4.0 \mathrm{~s}\), what is its acceleration in \(\mathrm{m} / \mathrm{s}^2\) ? Express the answer in terms of "g's," where \(1.00 \mathrm{~g}=9.80 \mathrm{~m} / \mathrm{s}^2\).

The position of a racing car, which starts from rest at t = 0 and moves in a straight line, is given as a function of time in the following Table. Estimate (a) its velocity and (b) its acceleration as a function of time. Display each in a Table and on a graph. t(s) 0 0.25 0.50 0.75 1.00 1.50 2.00 2.50 x(m) 0 0.11 0.46 1.06 1.94 4.62 8.55 13.79 t(s) 3.00 3.50 4.00 4.50 5.00 5.50 6.00 x(m) 20.36 28.31 37.65 48.37 60.30 73.26 87.16

A car accelerates from \(13 \mathrm{~m} / \mathrm{s}\) to \(25 \mathrm{~m} / \mathrm{s}\) in \(6.0 \mathrm{~s}\). What was its acceleration? How far did it travel in this time? Assume constant acceleration.

(I) A car slows down from 23 m/s to rest in a distance of 85 m. What was its acceleration, assumed constant?

Problem 23P A light plane must reach a speed of 33 m/s for takeoff. How long a runway is needed if the (constant) acceleration is 3.0 m/s2?

Problem 24P A world-class sprinter can burst out of the blocks to essentially top speed (of about 11.5 m/s) in the first 15.0 m of the race. What is the average acceleration of this sprinter, and how long does it take her to reach that speed?

Problem 25P A car slows down uniformly from a speed of 21.0 m/s to rest in 6.00 s. How far did it travel in that time?

(II) In coming to a stop, a car leaves skid marks \(92 \mathrm{~m}\) long on the highway. Assuming a deceleration of \(7.00 \mathrm{~m} / \mathrm{s}^2\), estimate the speed of the car just before braking.

A car traveling 85 km/h strikes a tree. The front end of the car compresses and the driver comes to rest after traveling 0.80 m. What was the average acceleration of the driver during the collision? Express the answer in terms of “g’s,” where \(1.00~g = 9.80~\mathrm{m/s^2}\).

(II) Determine the stopping distances for a car with an initial speed of 95 km/h and human reaction time of 1.0s, for an acceleration (a) \(a = ?4.0 \ \mathrm {m/s}^2\); (b) \(a = ?8.0 \ \mathrm {m/s}^2\).

Show that the equation for the stopping distance of a car is \(d_{s}=v_{o} t_{R}-v_{0}^{2} /(2 \alpha)\), where \(v_{o}\) is the initial speed of the car, \(t_{R}\) is the driver’s reaction time, and \(\alpha\) is the constant acceleration (and is negative). Equation Transcription: Text Transcription: d_{s}=v_{o} t_{R}-v_{0}^{2} /(2 \alpha) v_{o} t_{R} \alpha

Problem 30P A car is behind a truck going 25 m/s on the highway. The car’s driver looks for an opportunity to pass, guessing that his car can accelerate at 1.0 m/s2. He gauges that he has to cover the 20-m length of the truck, plus 10 m clear room at the rear of the truck and 10 m more at the front of it. In the oncoming lane, he sees a car approaching, probably also traveling at 25 m/s. He estimates that the car is about 400 m away. Should he attempt the pass? Give details.

A runner hopes to complete the 10,000-m run in less than 30.0 min. After exactly 27.0 min, there are still 1100 m to go. The runner must then accelerate at \(0.20 \ \mathrm {m/s}^2\) for how many seconds in order to achieve the desired time?

(III) A person driving her car at 45 km/h approaches an intersection just as the traffic light turns yellow. She knows that the yellow light lasts only 2.0 s before turning red, and she is 28 m away from the near side of the intersection (Fig. 2–31). Should she try to stop, or should she speed up to cross the intersection before the light turns red? The intersection is 15 m wide. Her car’s maximum deceleration is \(-5.8 \mathrm{~m} / \mathrm{s}^{2}\), whereas it can accelerate from 45 km/h to 65 km/h in 6.0 s. Ignore the length of her car and her reaction time. Equation Transcription: Text Transcription: -5.8 m/s2

(I) A stone is dropped from the top of a cliff. It hits the ground below after 3.25 s. How high is the cliff?

If a car rolls gently \(\left(v_0=0\right)\) off a vertical cliff, how long does it take it to reach \(85 \mathrm{~km} / \mathrm{h}\)?

(I) Estimate (a) how long it took King Kong to fall straight down from the top of the Empire State Building (380 m high), and (b) his velocity just before “landing”?

(II) A baseball is hit nearly straight up into the air with a speed of 22 m/s. (a) How high does it go? (b) How long is it in the air?

(II) A ballplayer catches a ball 3.0 s after throwing it vertically upward. With what speed did he throw it, and what height did it reach?

(II) An object starts from rest and falls under the influence of gravity. Draw graphs of (a) its speed and (b) the distance it has fallen, as a function of time from t = 0 to t = 5.00 s. Ignore air resistance.

Problem 39P A helicopter is ascending vertically with a speed of 5.20 m/s. At a height of 125 m above the Earth, a package is dropped from a window. How much time does it take for the package to reach the ground? [Hint: The package’s initial speed equals the helicopter’s.]

(II) If air resistance is neglected, show (algebraically) that a ball thrown vertically upward with a speed \(v_0\) will have the same speed, \(v_0\), when it comes back down to the starting point.

A stone is thrown vertically upward with a speed of 18.0 m/s. (a) How fast is it moving when it reaches a height of 11.0 m? (b) How long is required to reach this height? (c) Why are there two answers to (b)?

Estimate the time between each photoflash of the apple in Fig. 2–18 (or number of photoflashes per second). Assume the apple is about 10 cm in diameter. [Hint: Use two apple positions, but not the unclear ones at the top.]

A falling stone takes \(0.28 \mathrm{~s}\) to travel past a window \(2.2 \mathrm{~m}\) tall (Fig. 2-32). From what height above the top of the window did the stone fall?

Problem 45P A rock is dropped from a sea cliff, and the sound of it striking the ocean is heard 3.2 s later. If the speed of sound is 340 m/s, how high is the cliff?

Suppose you adjust your garden hose nozzle for a hard stream of water. You point the nozzle vertically upward at a height of 1.5 m above the ground (Fig. 2–33). When you quickly move the nozzle away from the vertical, you hear the water striking the ground next to you for another 2.0 s. What is the water speed as it leaves the nozzle?

(III) A stone is thrown vertically upward with a speed of 12.0 m/s from the edge of a cliff 70.0 m high (Fig. 2–34). (a) How much later does it reach the bottom of the cliff? (b) What is its speed just before hitting? (c) What total distance did it travel?

(III) A baseball is seen to pass upward by a window \(28 \mathrm{~m}\) above the street with a vertical speed of \(13 \mathrm{~m} / \mathrm{s}\). If the ball was thrown from the street, (a) what was its initial speed, (b) what altitude does it reach, (c) when was it thrown, and (d) when does it reach the street again?

Figure 2-29 shows the velocity of a train as a function of time. (a) At what time was its velocity greatest? (b) During what periods, if any, was the velocity constant? (c) During what periods, if any, was the acceleration constant? (d) When was the magnitude of the acceleration greatest?

The position of a rabbit along a straight tunnel as a function of time is plotted in Fig. 2–28. What is its instantaneous velocity (a) at \(t=10.0 \mathrm{~s}\) and (b) at \(t=30.0 \mathrm{~s}\)? What is its average velocity (c) between \(t=0 \text { and } t=5.0 \mathrm{~s}\), (d) between \(t=25.0 \mathrm{~s} \text { and } t=30.0 \mathrm{~s}\), and (e) between \(t=40.0 \mathrm{~s} \text { and } t=50.0 \mathrm{~s}\)? Equation Transcription: Text Transcription: t=10.0 s t=30.0 s t=0 and t=5.0 s t=25.0 s and t=30.0 s t=40.0 s and t=50.0 s

(II) In Fig. 2-28, (a) during what time periods, if any, is the velocity constant? (b) At what time is the velocity greatest? (c) At what time, if any, is the velocity zero? (d) Does the object move in one direction or in both directions during the time shown?

A certain type of automobile can accelerate approximately as shown in the velocity-time graph of Fig. 2-35. (The short flat spots in the curve represent shifting of the gears.) (a) Estimate the average acceleration of the car in second gear and in fourth gear. (b) Estimate how far the car traveled while in fourth gear.

Estimate the average acceleration of the car in the previous Problem (Fig. 2–35) when it is in (a) first, (b) third, and (c) fifth gear. (d) What is its average acceleration through the first four gears?

In Fig. 2–29, estimate the distance the object traveled during (a) the first minute, and (b) the second minute.

Construct the v vs. t graph for the object whose displacement as a function of time is given by Fig. 2–28.

FIGURE 2–36 is a position versus time graph for the motion of an object along the x axis. Consider the time interval from A to B. (a) Is the object moving in the positive or negative direction? (b) Is the object speeding up or slowing down? (c) Is the acceleration of the object positive or negative? Now consider the time interval from D to E. (d) Is the object moving in the positive or negative direction? (e) Is the object speeding up or slowing down? (f) Is the acceleration of the object positive or negative? (g) Finally, answer these same three questions for the time interval from C to D.

A person jumps from a fourth-story window 15.0 m above a firefighter’s safety net. The survivor stretches the net 1.0 m before coming to rest, Fig. 2–37. (a) What was the average deceleration experienced by the survivor when she was slowed to rest by the net? (b) What would you do to make it “safer” (that is, to generate a smaller deceleration): would you stiffen or loosen the net? Explain.

A person who is properly constrained by an over-the shoulder seat belt has a good chance of surviving a car collision if the deceleration does not exceed about 30 ‘’\(\mathrm{~g}\)'s" \(\left(1.0 \mathrm{~g}=9.8 \mathrm{~m} / \mathrm{s}^2\right)\). Assuming uniform deceleration of this value, calculate the distance over which the front end of the car must be designed to collapse if a crash brings the car to rest from \(100 \mathrm{~km} / \mathrm{h}\).

Problem 60GP Agent Bond is standing on a bridge, 12 m above the road below, and his pursuers are getting too close for comfort. He spots a flatbed truck approaching at 25m/s, which he measures by knowing that the telephone poles the truck is passing are 25 m apart in this country. The bed of the truck is 1.5 m above the road, and Bond quickly calculates how many poles away the truck should be when he jumps down from the bridge onto the truck to make his getaway. How many poles is it?

Suppose a car manufacturer tested its cars for front-end collisions by hauling them up on a crane and dropping them from a certain height. (a) Show that the speed just before a car hits the ground, after falling from rest a vertical distance H, is given by \(\sqrt{2 g H}\). What height corresponds to a collision at (b) 60 km/h? (c) 100 km/h?

Problem 62GP Every year the Earth travels about 109 km as it orbits the Sun. What is Earth’s average speed in km/h?

A 95-m-long train begins uniform acceleration from rest. The front of the train has a speed of 25 m/s when it passes a railway worker who is standing 180 m from where the front of the train started. What will be the speed of the last car as it passes the worker? (See Fig. 2–38.)

Problem 64GP A person jumps off a diving board 4.0 m above the water’s surface into a deep pool. The person’s downward motion stops 2.0 m below the surface of the water. Estimate the average deceleration of the person while under the water.

Problem 65GP In the design of a rapid transit system, it is necessary to balance the average speed of a train against the distance between stops. Tire more stops there are, the slower the train’s average speed. To get an idea of this problem, calculate the time it takes a train to make a 9.0-km trip in two situations: (a) the stations at which the trains must stop are 1.8 km apart (a total of 6 stations, including those at the ends); and (b) the stations are 3.0 km apart (4 stations total). Assume that at each station the train accelerates at a rate of 1.1 m/s2 until it reaches 90 km/h, then stays at this speed until its brakes are applied for arrival at the next station, at which time it decelerates at ?2.0 m/s2. Assume it stops at each intermediate station for 20 s.

Pelicans tuck their wings and free fall straight down when diving for fish. Suppose a pelican starts its dive from a height of 16.0 m and cannot change its path once committed. If it takes a fish 0.20 s to perform evasive action, at what minimum height must it spot the pelican to escape? Assume the fish is at the surface of the water.

In putting, the force with which a golfer strikes a ball is planned so that the ball will stop within some small distance of the cup, say, 1.0 m long or short, in case the putt is missed. Accomplishing this from an uphill lie (that is, putting downhill, see Fig. 2–39) is more difficult than from a downhill lie. To see why, assume that on a particular green the ball decelerates constantly at \(2.0 \mathrm{~m} / \mathrm{s}^{2}\) going downhill, and constantly at \(3.0 \mathrm{~m} / \mathrm{s}^{2}\) going uphill. Suppose we have an uphill lie 7.0 m from the cup. Calculate the allowable range of initial velocities we may impart to the ball so that it stops in the range 1.0 m short to 1.0 m long of the cup. Do the same for a downhill lie 7.0 m from the cup. What in your results suggests that the downhill putt is more difficult? Equation Transcription: Text Transcription: 2.0 m/s2 3.0 m/s2

A stone is dropped from the roof of a high building. A second stone is dropped \(1.50 \mathrm{~s}\) later. How far apart are the stones when the second one has reached a speed of \(12.0 \mathrm{~m} / \mathrm{s}\) ?

Problem 68GP A fugitive tries to hop on a freight train traveling at a constant speed of 6.0 m/s. Just as an empty box car passes him, the fugitive starts from rest and accelerates at a = 4.0 m/s2 to his maximum speed of 8.0 m/s. (a) How long does it take him to catch up to the empty box car? (b) What is the distance traveled to reach the box car?

Problem 70GP A race car driver must average 200.0 km/h over the course of a time trial lasting ten laps. If the first nine laps were done at 198.0 km/h, what average speed must be maintained for the last lap?

Problem 71GP A bicyclist in the Tour de France crests a mountain pass as he moves at 18 km/h. At the bottom, 4.0 km farther, his speed is 75 km/h. What was his average acceleration (in m/s2) while riding down the mountain?

Two children are playing on two trampolines. The first child can bounce up one-and-a-half times higher than the second child. The initial speed up of the second child is 5.0 m/s. (a) Find the maximum height the second child reaches. (b) What is the initial speed of the first child? (c) How long was the first child in the air?

An automobile traveling 95 km/h overtakes a 1.10-km-long train traveling in the same direction on a track parallel to the road. If the train’s speed is 75 km/h, how long does it take the car to pass it, and how far will the car have traveled in this time? See Fig. 2–40. What are the results if the car and train are traveling in opposite directions?

A baseball pitcher throws a baseball with a speed of \(44 \mathrm{~m} / \mathrm{s}\). In throwing the baseball, the pitcher accelerates the ball through a displacement of about \(3.5 \mathrm{~m}\), from behind the body to the point where it is released (Fig. 2-41). Estimate the average acceleration of the ball during the throwing motion.

A rocket rises vertically, from rest, with an acceleration of \(3.2~\mathrm {m/s}^2\) until it runs out of fuel at an altitude of 1200 m. After this point, its acceleration is that of gravity, downward. (a) What is the velocity of the rocket when it runs out of fuel? (b) How long does it take to reach this point? (c) What maximum altitude does the rocket reach? (d) How much time (total) does it take to reach maximum altitude? (e) With what velocity does the rocket strike the Earth? (f) How long (total) is it in the air?

Consider the street pattern shown in Fig. 2–42. Each intersection has a traffic signal, and the speed limit is 50 km/h. Suppose you are driving from the west at the speed limit. When you are 10 m from the first intersection, all the lights turn green. The lights are green for 13 s each. (a) Calculate the time needed to reach the third stoplight. Can you make it through all three lights without stopping? (b) Another car was stopped at the first light when all the lights turned green. It can accelerate at the rate of \(2.0 \mathrm{~m} / \mathrm{s}^{2}\) to the speed limit. Can the second car make it through all three lights without stopping? Equation Transcription: Text Transcription: 2.0 m/s2

A police car at rest, passed by a speeder traveling at a constant 120 km/h, takes off in hot pursuit. The police officer catches up to the speeder in 750 m, maintaining a constant acceleration. (a) Qualitatively plot the position vs. time graph for both cars from the police car’s start to the catch-up point. Calculate (b) how long it took the police officer to overtake the speeder, (c) the required police car acceleration, and (d) the speed of the police car at the overtaking point.

Problem 78GP A stone is dropped from the roof of a building; 2.00 s after that, a second stone is thrown straight down with an initial speed of 25.0 m/s, and the two stones land at the same time. (a) How long did it take the first stone to reach the ground? (b) How high is the building? (c) What are the speeds of the two stones just before they hit the ground?

Problem 79GP Two stones are thrown vertically up at the same time. The first stone is thrown with an initial velocity of 11.0 m/s from a 12th-floor balcony of a building and hits the ground after 4.5 s. With what initial velocity should the second stone be thrown from a 4th-floor balcony so that it hits the ground at the same time as the first stone? Make simple assumptions, like equal-height floors.

Problem 80GP If there were no air resistance, how long would it take a free-falling parachutist to fall from a plane at 3200 m to an altitude of 350 m, where she will pull her ripcord? What would her speed be at 350 m? (In reality, the air resistance will restrict her speed to perhaps 150 km/h.)

Problem 81GP A fast-food restaurant uses a conveyor belt to send the burgers through a grilling machine. If the grilling machine is 1.1 m long and the burgers require 2.5 min to cook, how fast must the conveyor belt travel? If the burgers are spaced 15 cm apart, what is the rate of burger production (in burgers/min)?

Bill can throw a ball vertically at a speed 1.5 times faster than Joe can. How many times higher will Bill’s ball go than Joe’s?

You stand at the top of a cliff while your friend stands on the ground below you. You drop a ball from rest and see that it takes 1.2 s for the ball to hit the ground below. Your friend then picks up the ball and throws it up to you, such that it just comes to rest in your hand. What is the speed with which your friend threw the ball?

Two students are asked to find the height of a particular building using a barometer. Instead of using the barometer as an altitude-measuring device, they take it to the roof of the building and drop it off, timing its fall. One student reports a fall time of 2.0 s, and the other, 2.3 s. How much difference does the 0.3 s make for the estimates of the building’s height?