At the edge of a roof you throw ball 1 upward with an

Referring to Figure 220, you walk from your home to the library, then to the park. (a) What is the distance traveled? (b) What is your displacement?

The two tennis players shown in Figure 221walk to the net to congratulate one another. (a)Find the distance traveled and the displacement of player A. (b) Repeat for player B.

The golfer in Figure 222sinks the ball in two putts, as shown. What are (a) the distance traveled by the ball, and (b) the displacement of the ball?

In Figure 220, you walk from the park to your friends house, then back to your house. What is your (a)distance traveled, and (b) displacement?

Ajogger runs on the track shown in Figure 223. Neglecting the curvature of the corners, (a) what is the distance traveled and the displacement in running from point A to point B? (b) Find the distance and displacement for a complete circuit of the track.

A child rides a pony on a circular track whose radius is 4.5 m. (a) Find the distance traveled and the displacement after the child has gone halfway around the track. (b) Does the distance traveled increase, decrease, or stay the same when the child completes one circuit of the track? Explain. (c) Does the displacement increase, decrease, or stay the same when the child completes one circuit of the track? Explain. (d)Find the distance and displacement after a complete circuit of the track.

Predict/Explain You drive your car in a straight line at 15 m/s for 10 kilometers, then at 25 m/s for another 10 kilometers.(a)Is your average speed for the entire trip more than, less than, or equal to 20 m/s? (b) Choose the best explanation from among the following: I. More time is spent at 15 m/s than at 25 m/s. II. The average of 15 m/s and 25 m/s is 20 m/s. III. Less time is spent at 15 m/s than at 25 m/s.

You drive your car in a straight line at 15 m/s for 10 minutes, then at 25 m/s for another 10 minutes. (a)Is your average speed for the entire trip more than, less than, or equal to 20 m/s? (b)Choose the bestexplanation from among the following: I. More time is required to drive at 15 m/s than at 25 m/s. II. Less distance is covered at 25 m/s than at 15 m/s. III. Equal time is spent at 15 m/s and 25 m/s.

Joseph DeLoach of the United States set an Olympic record in 1988 for the 200-meter dash with a time of 19.75 seconds. What was his average speed? Give your answer in meters per second and miles per hour.

In 1992 Zhuang Yong of China set a womens Olympic record in the 100-meter freestyle swim with a time of 54.64 seconds. What was her average speed in m/s and mi/h?

Kangaroos have been clocked at speeds of 65 km/h. (a) How far can a kangaroo hop in 3.2 minutes at this speed? (b)How long will it take a kangaroo to hop 0.25 km at this speed?

Rubber Ducks Asevere storm on January 10, 1992, caused a cargo ship near the Aleutian Islands to spill 29,000 rubber ducks and other bath toys into the ocean. Ten months later hundreds of rubber ducks began to appear along the shoreline near Sitka, Alaska, roughly 1600 miles away. What was the approximate average speed of the ocean current that carried the ducks to shore in (a)m/s and (b)mi/h? (Rubber ducks from the same spill began to appear on the coast of Maine in July 2003.)

Radio waves travel at the speed of light, approximately 186,000 miles per second. How long does it take for a radio message to travel from Earth to the Moon and back? (See the inside back cover for the necessary data.)

It was a dark and stormy night, when suddenly you saw a ash of lightning. Three-and-a-half seconds later you heard the thunder. Given that the speed of sound in air is about 340 m/s, how far away was the lightning bolt?

Nerve Impulses The human nervous system can propagate nerve impulses at about . Estimate the time it takes for a nerve impulse generated when your nger touches a hot object to travel to your brain.

Estimate how fast your hair grows in miles per hour.

A nch rides on the back of a Galapagos tortoise, which walks at the stately pace of 0.060 m/s. After 1.2 minutes the nch tires of the tortoises slow pace, and takes ight in the same direction for another 1.2 minutes at 12 m/s. What was the average speed of the nch for this 2.4-minute interval?

You jog at 9.5 km/h for 8.0 km, then you jump into a car and drive an additional 16 km. With what average speed must you drive your car if your average speed for the entire 24 km is to be 22 km/h?

Adog runs back and forth between its two owners, who are walking toward one another (Figure 224). The dog starts running when the owners are 10.0 m apart. If the dog runs with a speed of 3.0 m/s, and the owners each walk with a speed of 1.3 m/s, how far has the dog traveled when the owners meet?

You drive in a straight line at 20.0 m/s for 10.0 minutes, then at 30.0 m/s for another 10.0 minutes. (a)Is your average speed 25.0 m/s, more than 25.0 m/s, or less than 25.0 m/s? Explain. (b) Verify your answer to part (a) by calculating the average speed.

In heavy rush-hour trafc you drive in a straight line at 12 m/s for 1.5 minutes, then you have to stop for 3.5 minutes, and nally you drive at 15 m/s for another 2.5 minutes. (a) Plot a positionversus-time graph for this motion. Your plot should extend from to minutes. (b)Use your plot from part (a) to calculate the average velocity between and minutes.

You drive in a straight line at 20.0 m/s for 10.0 miles, then at 30.0 m/s for another 10.0 miles. (a) Is your average speed 25.0 m/s, more than 25.0 m/s, or less than 25.0 m/s? Explain. (b) Verify your answer to part (a) by calculating the average speed.

An expectant father paces back and forth, producing the position-versus-time graph shown in Figure 225. Without performing a calculation, indicate whether the fathers velocity is positive, negative, or zero on each of the following segments of the graph: (a)A, (b) B, (c) C, and (d) D. Calculate the numerical value of the fathers velocity for the segments (e)A,(f)B,(g)C, and (h)D, and show that your results verify your answers to parts (a)(d).

The position of a particle as a function of time is given by . (a) Plot x versus t for to . (b) Find the average velocity of the particle from to . (c) Find the average speed from to .

The position of a particle as a function of time is given by . (a) Plot x versus t for to . (b) Find the average velocity of the particle from to . (c) Find the average speed from to .

Atennis player moves back and forth along the baseline while waiting for her opponent to serve, producing the positionversus-time graph shown in Figure 226.(a)Without performing a calculation, indicate on which of the segments of the graph, A, B, or C, the player has the greatest speed. Calculate the players speed for (b) segment A, (c) segment B, and (d) segment C, and show that your results verify your answers to part (a).

On your wedding day you leave for the church 30.0 minutes before the ceremony is to begin, which should be plenty of time since the church is only 10.0 miles away. On the way, however, you have to make an unanticipated stop for construction work on the road. As a result, your average speed for the rst 15 minutes is only 5.0 mi/h. What average speed do you need for the rest of the trip to get you to the church on time?

The position-versus-time plot of a boat positioning itself next to a dock is shown in Figure 227. Rank the six points indicated in the plot in order of increasing value of the velocity v, starting with the most negative. Indicate a tie with an equal sign.

The position of a particle as a function of time is given by .(a)Plotxversustfor time from to . (b) Find the average velocity of the particle from to . (c) Find the average velocity from to . (d)Do you expect the instantaneous velocity at to be closer to 0.54 m/s, 0.56 m/s, or 0.58 m/s? Explain.

The position of a particle as a function of time is given by . (a) Plot x versus t for time from to . (b) Find the average velocity of the particle from to . (c) Find the average velocity from to . (d) Do you expect the instantaneous velocity at to be closer to , or ? Explain.

Predict/Explain Two bows shoot identical arrows with the same launch speed. To accomplish this, the string in bow 1 must be pulled back farther when shooting its arrow than the string in bow 2. (a) Is the acceleration of the arrow shot by bow 1 greater than, less than, or equal to the acceleration of the arrow shot by bow 2? (b) Choose the best explanation from among the following: I. The arrow in bow 2 accelerates for a greater time. II. Both arrows start from rest. III. The arrow in bow 1 accelerates for a greater time.

A747 airliner reaches its takeoff speed of 173 mi/h in 35.2 s. What is the magnitude of its average acceleration?

At the starting gun, a runner accelerates at for 5.2 s. The runners acceleration is zero for the rest of the race. What is the speed of the runner (a)at , and (b)at the end of the race?

A jet makes a landing traveling due east with a speed of 115 m/s. If the jet comes to rest in 13.0 s, what are the magnitude and direction of its average acceleration?

Acar is traveling due north at 18.1 m/s. Find the velocity of the car after 7.50 s if its acceleration is (a) due north, or (b) due south.

A motorcycle moves according to the velocity-versus-time graph shown in Figure 228. Find the average acceleration of the motorcycle during each of the following segments of the motion: (a)A, (b) B, and (c) C.

A person on horseback moves according to the velocityversus-time graph shown in Figure 229. Find the displacement of the person for each of the following segments of the motion: (a)A, (b) B, and (c) C.

Running with an initial velocity of , a horse has an average acceleration of . How long does it take for the horse to decrease its velocity to

Assume that the brakes in your car create a constant deceleration of regardless of how fast you are driving. If you double your driving speed from 16 m/s to 32 m/s, (a) does the time required to come to a stop increase by a factor of two or a factor of four? Explain. Verify your answer to part (a) by calculating the stopping times for initial speeds of (b)16 m/s and (c)32 m/s.

In the previous problem, (a) does the distance needed to stop increase by a factor of two or a factor of four? Explain. Verify your answer to part (a) by calculating the stopping distances for initial speeds of (b) 16 m/s and (c) 32 m/s.

As a train accelerates away from a station, it reaches a speed of 4.7 m/s in 5.0 s. If the trains acceleration remains constant, what is its speed after an additional 6.0 s has elapsed?

A particle has an acceleration of for 0.300 s. At the end of this time the particles velocity is . What was the particles initial velocity?

Landing with a speed of 81.9 m/s, and traveling due south, a jet comes to rest in 949 m. Assuming the jet slows with constant acceleration, nd the magnitude and direction of its acceleration.

When you see a trafc light turn red, you apply the brakes until you come to a stop. If your initial speed was 12 m/s, and you were heading due west, what was your average velocity during braking? Assume constant deceleration.

Aball is released at the point on an inclined plane with a nonzero initial velocity. After being released, the ball moves with constant acceleration. The acceleration and initial velocity of the ball are described by one of the following four cases: case 1, ; case 2, ; case 3, ; case 4, . (a) In which of these cases will the ball denitely pass at some later time? (b)In which of these cases is more information needed to determine whether the ball will cross ? (c) In which of these cases will the ball come to rest momentarily at some time during its motion?

Suppose the car in Problem 44 comes to rest in 35 m. How much time does this take?

Starting from rest, a boat increases its speed to 4.12 m/s with constant acceleration. (a)What is the boats average speed? (b)If it takes the boat 4.77 s to reach this speed, how far has it traveled?

Acheetah can accelerate from rest to 25.0 m/s in 6.22 s. Assuming constant acceleration, (a)how far has the cheetah run in this time? (b)After sprinting for just 3.11 s, is the cheetahs speed 12.5 m/s, more than 12.5 m/s, or less than 12.5 m/s? Explain. (c) What is the cheetahs average speed for the rst 3.11 s of its sprint? For the second 3.11 s of its sprint? (d) Calculate the distance covered by the cheetah in the rst 3.11 s and the second 3.11 s.

Achild slides down a hill on a toboggan with an acceleration of . If she starts at rest, how far has she traveled in (a) 1.0 s, (b) 2.0 s, and (c) 3.0 s?

The Detonator On a ride called the Detonator at Worlds of Fun in Kansas City, passengers accelerate straight downward from rest to 45 mi/h in 2.2 seconds. What is the average acceleration of the passengers on this ride?

Air Bags Air bags are designed to deploy in 10 ms. Estimate the acceleration of the front surface of the bag as it expands. Express your answer in terms of the acceleration of gravity g.

Jules Verne In his novel From the Earth to the Moon (1866), Jules Verne describes a spaceship that is blasted out of a cannon, called the Columbiad, with a speed of 12,000 yards/s. The Columbiad is 900 ft long, but part of it is packed with powder, so the spaceship accelerates over a distance of only 700 ft. Estimate the acceleration experienced by the occupants of the spaceship during launch. Give your answer in . (Verne realized that the travelers would. . . encounter a violent recoil, but he probably didnt know that people generally lose consciousness if they experience accelerations greater than about .)

Bacterial Motion Approximately 0.1% of the bacteria in an adult humans intestines are Escherichia coli. These bacteria have been observed to move with speeds up to and maximum accelerations of . Suppose an E. coli bacterium in your intestines starts at rest and accelerates at . How much (a) time and (b) distance are required for the bacterium to reach a speed of ?

Two cars drive on a straight highway. At time , car 1 passes mile marker 0 traveling due east with a speed of 20.0 m/s. At the same time, car 2 is 1.0 km east of mile marker 0 traveling at 30.0 m/s due west. Car 1 is speeding up with an acceleration of magnitude , and car 2 is slowing down with an acceleration of magnitude . (a)Write x-versust equations of motion for both cars, taking east as the positive direction. (b)At what time do the cars pass next to one another?

A Meteorite Strikes On October 9, 1992, a 27-pound meteorite struck a car in Peekskill, NY, leaving a dent 22 cm deep in the trunk. If the meteorite struck the car with a speed of 130 m/s, what was the magnitude of its deceleration, assuming it to be constant?

A rocket blasts off and moves straight upward from the launch pad with constant acceleration. After 3.0 s the rocket is at a height of 77 m. (a)What are the magnitude and direction of the rockets acceleration? (b) What is its speed at this time?

You are driving through town at 12.0 m/s when suddenly a ball rolls out in front of you. You apply the brakes and begin decelerating at . (a)How far do you travel before stopping? (b) When you have traveled only half the distance in part (a), is your speed 6.0 m/s, greater than 6.0 m/s, or less than 6.0 m/s? Support your answer with a calculation.

You are driving through town at 16 m/s when suddenly a car backs out of a driveway in front of you. You apply the brakes and begin decelerating at . (a) How much time does it take to stop? (b) After braking half the time found in part (a), is your speed 8.0 m/s, greater than 8.0 m/s, or less than 8.0 m/s? Support your answer with a calculation. (c) If the car backing out was initially 55 m in front of you, what is the maximum reaction time you can have before hitting the brakes and still avoid hitting the car?

A Tongues Acceleration When a chameleon captures an insect, its tongue can extend 16 cm in 0.10 s. (a)Find the magnitude of the tongues acceleration, assuming it to be constant. (b)In the rst 0.050 s, does the tongue extend 8.0 cm, more than 8.0 cm, or less than 8.0 cm? Support your conclusion with a calculation.

Coasting due west on your bicycle at 8.4 m/s, you encounter a sandy patch of road 7.2 m across. When you leave the sandy patch your speed has been reduced by 2.0 m/s to 6.4 m/s. (a) Assuming the sand causes a constant acceleration, what was the bicycles acceleration in the sandy patch? Give both magnitude and direction. (b)How long did it take to cross the sandy patch? (c) Suppose you enter the sandy patch with a speed of only 5.4 m/s. Is your nal speed in this case 3.4 m/s, more than 3.4 m/s, or less than 3.4 m/s? Explain.

Surviving a Large Deceleration On July 13, 1977, while on a test drive at Britains Silverstone racetrack, the throttle on David Purleys car stuck wide open. The resulting crash subjected Purley to the greatest g-force ever survived by a humanhe decelerated from 173 km/h to zero in a distance of only about 0.66 m. Calculate the magnitude of the acceleration experienced by Purley (assuming it to be constant), and express your answer in units of the acceleration of gravity,

Aboat is cruising in a straight line at a constant speed of 2.6 m/s when it is shifted into neutral. After coasting 12 m the engine is engaged again, and the boat resumes cruising at the reduced constant speed of 1.6 m/s. Assuming constant acceleration while coasting, (a)how long did it take for the boat to coast the 12 m? (b) What was the boats acceleration while it was coasting?(c)When the boat had coasted for 6.0 m, was its speed 2.1 m/s, more than 2.1 m/s, or less than 2.1 m/s? Explain.

Amodel rocket rises with constant acceleration to a height of 3.2 m, at which point its speed is 26.0 m/s. (a) How much time does it take for the rocket to reach this height? (b)What was the magnitude of the rockets acceleration? (c) Find the height and speed of the rocket 0.10 s after launch.

The infamous chicken is dashing toward home plate with a speed of 5.8 m/s when he decides to hit the dirt. The chicken slides for 1.1 s, just reaching the plate as he stops (safe, of course). (a) What are the magnitude and direction of the chickens acceleration? (b) How far did the chicken slide?

A bicyclist is nishing his repair of a at tire when a friend rides by with a constant speed of 3.5 m/s. Two seconds later the bicyclist hops on his bike and accelerates at until he catches his friend. (a)How much time does it take until he catches his friend? (b)How far has he traveled in this time? (c)What is his speed when he catches up?

A car in stop-and-go trafc starts at rest, moves forward 13 m in 8.0 s, then comes to rest again. The velocity-versus-time plot for this car is given in Figure 230. What distance does the car cover in (a)the rst 4.0 seconds of its motion and (b)the last 2.0 seconds of its motion? (c) What is the constant speed V that characterizes the middle portion of its motion?

Acar and a truck are heading directly toward one another on a straight and narrow street, but they avoid a head-on collision by simultaneously applying their brakes at . The resulting velocity-versus-time graphs are shown in Figure 231. What is the separation between the car and the truck when they have come to rest, given that at the car is at and the truck is at ? (Note that this information determines which line in the graph corresponds to which vehicle.)

In a physics lab, students measure the time it takes a small cart to slide a distance of 1.00 m on a smooth track inclined at an angle above the horizontal. Their results are given in the following table. (a) Find the magnitude of the carts acceleration for each angle. (b) Show that your results for part (a) are in close agreement with the formula, . (We will derive this formula in Chapter 5.)

At the edge of a roof you throw ball 1 upward with an initial speed ; a moment later you throw ball 2 downward with the same initial speed. The balls land at the same time. Which of the following statements is true for the instant just before the balls hit the ground? A. The speed of ball 1 is greater than the speed of ball 2; B.The speed of ball 1 is equal to the speed of ball 2; C. The speed of ball 1 is less than the speed of ball 2.

Legend has it that Isaac Newton was hit on the head by a falling apple, thus triggering his thoughts on gravity. Assuming the story to be true, estimate the speed of the apple when it struck Newton.

The cartoon shows a car in free fall. Is the statement made in the cartoon accurate? Justify your answer.

Referring to the cartoon in Problem 71, how long would it take for the car to go from 0 to 30 mi/h?

Jordans Jump Michael Jordans vertical leap is reported to be 48 inches. What is his takeoff speed? Give your answer in meters per second

Gulls are often observed dropping clams and other shellsh from a height to the rocks below, as a means of opening the shells. If a seagull drops a shell from rest at a height of 14 m, how fast is the shell moving when it hits the rocks?

Avolcano launches a lava bomb straight upward with an initial speed of 28 m/s. Taking upward to be the positive direction, nd the speed and direction of motion of the lava bomb (a) 2.0 seconds and (b) 3.0 seconds after it is launched.

An Extraterrestrial Volcano The rst active volcano observed outside the Earth was discovered in 1979 on Io, one of the moons of Jupiter. The volcano was observed to be ejecting material to a height of about . Given that the acceleration of gravity on Io is , nd the initial velocity of the ejected material.

Measure Your Reaction Time Heres something you can try at homean experiment to measure your reaction time. Have a friend hold a ruler by one end, letting the other end hang down vertically. At the lower end, hold your thumb and index nger on either side of the ruler, ready to grip it. Have your friend release the ruler without warning. Catch it as quickly as you can. If you catch the ruler 5.2 cm from the lower end, what is your reaction time?

Predict/Explain A carpenter on the roof of a building accidentally drops her hammer. As the hammer falls it passes two windows of equal height, as shown in Figure 232. (a) Is the increase in speed of the hammer as it drops past window 1 greater than, less than, or equal to the increase in speed as it drops past window 2? (b) Choose the best explanation from among the following: I. The greater speed at window 2 results in a greater increase in speed. II. Constant acceleration means the hammer speeds up the same amount for each window. III. The hammer spends more time dropping past window 1.

Predict/Explain Figure 233 shows a v-versus-t plot for the hammer dropped by the carpenter in Problem 78. Notice that the times when the hammer passes the two windows are indicated by shaded areas. (a) Is the area of the shaded region corresponding to window 1 greater than, less than, or equal to the area of the shaded region corresponding to window 2? (b) Choose the best explanation from among the following: I. The shaded area for window 2 is higher than the shaded area for window 1. II. The windows are equally tall. III. The shaded area for window 1 is wider than the shaded area for window 2.

Aball is thrown straight upward with an initial speed . When it reaches the top of its ight at height h, a second ball is thrown straight upward with the same initial speed. Do the balls cross paths at height , above , or below ?

Bill steps off a 3.0-m-high diving board and drops to the water below. At the same time, Ted jumps upward with a speed of 4.2 m/s from a 1.0-m-high diving board. Choosing the origin to be at the waters surface, and upward to be the positive x direction, write x-versus-t equations of motion for both Bill and Ted.

Repeat the previous problem, this time with the origin 3.0 m above the water, and with downward as the positive xdirection.

On a hot summer day in the state of Washington while kayaking, I saw several swimmers jump from a railroad bridge into the Snohomish River below. The swimmers stepped off the bridge, and I estimated that they hit the water 1.5 s later. (a) How high was the bridge? (b) How fast were the swimmers moving when they hit the water? (c) What would the swimmers drop time be if the bridge were twice as high?

Highest Water Fountain The worlds highest fountain of water is located, appropriately enough, in Fountain Hills, Arizona. The fountain rises to a height of 560 ft (5 feet higher than the Washington Monument). (a) What is the initial speed of the water? (b) How long does it take for water to reach the top of the fountain?

Wrongly called for a foul, an angry basketball player throws the ball straight down to the oor. If the ball bounces straight up and returns to the oor 2.8 s after rst striking it, what was the balls greatest height above the oor?

To celebrate a victory, a pitcher throws her glove straight upward with an initial speed of 6.0 m/s. (a)How long does it take for the glove to return to the pitcher? (b) How long does it take for the glove to reach its maximum height?

Standing at the edge of a cliff 32.5 m high, you drop a ball. Later, you throw a second ball downward with an initial speed of 11.0 m/s. (a) Which ball has the greater increase in speed when it reaches the base of the cliff, or do both balls speed up by the same amount? (b) Verify your answer to part (a) with a calculation.

You shoot an arrow into the air. Two seconds later (2.00 s) the arrow has gone straight upward to a height of 30.0 m above its launch point. (a) What was the arrows initial speed? (b) How long did it take for the arrow to rst reach a height of 15.0 m above its launch point?

While riding on an elevator descending with a constant speed of 3.0 m/s, you accidentally drop a book from under your arm. (a)How long does it take for the book to reach the elevator oor, 1.2 m below your arm? (b) What is the books speed relative to you when it hits the elevator oor?

A hot-air balloon is descending at a rate of 2.0 m/s when a passenger drops a camera. If the camera is 45 m above the ground when it is dropped, (a)how long does it take for the camera to reach the ground, and (b) what is its velocity just before it lands? Let upward be the positive direction for this problem.

Standing side by side, you and a friend step off a bridge at different times and fall for 1.6 s to the water below. Your friend goes rst, and you follow after she has dropped a distance of 2.0 m. (a) When your friend hits the water, is the separation between the two of you 2.0 m, less than 2.0 m, or more than 2.0 m? (b)Verify your answer to part (a) with a calculation.

Amodel rocket blasts off and moves upward with an acceleration of until it reaches a height of 26 m, at which point its engine shuts off and it continues its ight in free fall. (a) What is the maximum height attained by the rocket? (b)What is the speed of the rocket just before it hits the ground? (c) What is the total duration of the rockets ight?

Hitting the High Striker Ayoung woman at a carnival steps up to the high striker, a popular test of strength where the contestant hits one end of a lever with a mallet, propelling a small metal plug upward toward a bell. She gives the mallet a mighty swing and sends the plug to the top of the striker, where it rings the bell. Figure 234 shows the corresponding position-versus-time plot for the plug. Using the information given in the plot, answer the following questions: (a) What is the average speed of the plug during its upward journey? (b) By how much does the speed of the plug decrease during its upward journey? (c) What is the initial speed of the plug? (Assume the plug to be in free fall during its upward motion, with no effects of air resistance or friction.)

While sitting on a tree branch 10.0 m above the ground, you drop a chestnut. When the chestnut has fallen 2.5 m, you throw a second chestnut straight down. What initial speed must you give the second chestnut if they are both to reach the ground at the same time?

In a well-known Jules Verne novel, Phileas Fogg travels around the world in 80 days. What was Mr. Foggs approximate average speed during his adventure?

An astronaut on the Moon drops a rock straight downward from a height of 1.25 m. If the acceleration of gravity on the Moon is , what is the speed of the rock just before it lands?

You jump from the top of a boulder to the ground 1.5 m below. Estimate your deceleration on landing.

A Supersonic Waterfall Geologists have learned of periods in the past when the Strait of Gibraltar closed off, and the Mediterranean Sea dried out and become a desert. Later, when the strait reopened, a massive saltwater waterfall was created. According to geologists, the water in this waterfall was supersonic; that is, it fell with speeds in excess of the speed of sound. Ignoring air resistance, what is the minimum height necessary to create a supersonic waterfall? (The speed of sound may be taken to be 340 m/s.)

At the edge of a roof you drop ball Afrom rest, and then throw ball B downward with an initial velocity of . Is the increase in speed just before the balls land more for ball A, more for ball B, or the same for each ball?

Suppose the two balls described in Problem 99 are released at the same time, with ball Adropped from rest and ball B thrown downward with an initial speed . Identify which of the ve plots shown in Figure 235corresponds to (a)ball Aand (b)ball B.

Astronauts on a distant planet throw a rock straight upward and record its motion with a video camera. After digitizing their video, they are able to produce the graph of height, y, versus time,t, shown in Figure 236.(a)What is the acceleration of gravity on this planet? (b) What was the initial speed of the rock?

Drop Tower NASAoperates a 2.2-second drop tower at the Glenn Research Center in Cleveland, Ohio. At this facility, experimental packages are dropped from the top of the tower, on the 8th oor of the building. During their 2.2 seconds of free fall, experiments experience a microgravity environment similar to that of a spacecraft in orbit. (a) What is the drop distance of a 2.2-s tower? (b) How fast are the experiments traveling when they hit the air bags at the bottom of the tower? (c) If the experimental package comes to rest over a distance of 0.75 m upon hitting the air bags, what is the average stopping acceleration?

A youngster bounces straight up and down on a trampoline. Suppose she doubles her initial speed from 2.0 m/s to 4.0 m/s. (a)By what factor does her time in the air increase? (b) By what factor does her maximum height increase? (c) Verify your answers to parts (a) and (b) with an explicit calculation.

At the 18th green of the U.S. Open you need to make a 20.5-ft putt to win the tournament. When you hit the ball, giving it an initial speed of 1.57 m/s, it stops 6.00 ft short of the hole. (a)Assuming the deceleration caused by the grass is constant, what should the initial speed have been to just make the putt? (b) What initial speed do you need to make the remaining 6.00-ft putt?

Apopular entertainment at some carnivals is the blanket toss (see photo, p. 39). (a) If a person is thrown to a maximum height of 28.0 ft above the blanket, how long does she spend in the air? (b) Is the amount of time the person is above a height of 14.0 ft more than, less than, or equal to the amount of time the person is below a height of 14.0 ft? Explain. (c)Verify your answer to part (b) with a calculation.

Referring to Conceptual Checkpoint 25, nd the separation between the rocks at (a) , (b) , and (c) , where time is measured from the instant the second rock is dropped. (d) Verify that the separation increases linearly with time.

Aglaucous-winged gull, ascending straight upward at 5.20 m/s, drops a shell when it is 12.5 m above the ground. (a) What are the magnitude and direction of the shells acceleration just after it is released? (b) Find the maximum height above the ground reached by the shell. (c) How long does it take for the shell to reach the ground? (d)What is the speed of the shell at this time?

Adoctor, preparing to give a patient an injection, squirts a small amount of liquid straight upward from a syringe. If the liquid emerges with a speed of 1.5 m/s, (a) how long does it take for it to return to the level of the syringe? (b) What is the maximum height of the liquid above the syringe?

Ahot-air balloon has just lifted off and is rising at the constant rate of 2.0 m/s. Suddenly one of the passengers realizes she has left her camera on the ground. Afriend picks it up and tosses it straight upward with an initial speed of 13 m/s. If the passenger is 2.5 m above her friend when the camera is tossed, how high is she when the camera reaches her?

In the previous problem, what is the minimum initial speed of the camera if it is to just reach the passenger? (Hint:When the camera is thrown with its minimum speed, its speed on reaching the passenger is the same as the speed of the passenger.)

Old Faithful Watching Old Faithful erupt, you notice that it takes a time t for water to emerge from the base of the geyser and reach its maximum height. (a)What is the height of the geyser, and (b)what is the initial speed of the water? Evaluate your expressions for (c) the height and (d) the initial speed for a measured time of 1.65 s.

A ball is thrown upward with an initial speed . When it reaches the top of its ight, at a height h, a second ball is thrown upward with the same initial velocity. (a) Sketch an x-versus-t plot for each ball. (b) From your graph, decide whether the balls cross paths at h/2, above h/2, or below h/2. (c) Find the height where the paths cross.

Weights are tied to each end of a 20.0-cm string. You hold one weight in your hand and let the other hang vertically a height h above the oor. When you release the weight in your hand, the two weights strike the ground one after the other with audible thuds. Find the value of h for which the time between release and the rst thud is equal to the time between the rst thud and the second thud.

Aball, dropped from rest, covers three-quarters of the distance to the ground in the last second of its fall. (a) From what height was the ball dropped? (b)What was the total time of fall?

A stalactite on the roof of a cave drips water at a steady rate to a pool 4.0 m below. As one drop of water hits the pool, a second drop is in the air, and a third is just detaching from the stalactite. (a) What are the position and velocity of the second drop when the rst drop hits the pool? (b) How many drops per minute fall into the pool?

You drop a ski glove from a height honto fresh snow, and it sinks to a depth dbefore coming to rest. (a)In terms of gand h, what is the speed of the glove when it reaches the snow? (b) What are the magnitude and direction of the gloves acceleration as it moves through the snow, assuming it to be constant? Give your answer in terms of g, h, and d.

To nd the height of an overhead power line, you throw a ball straight upward. The ball passes the line on the way up after 0.75 s, and passes it again on the way down 1.5 s after it was tossed. What are the height of the power line and the initial speed of the ball?

Suppose the rst rock in Conceptual Checkpoint 25 drops through a height h before the second rock is released from rest. Show that the separation between the rocks, S, is given by the following expression: In this result, the time t is measured from the time the second rock is dropped.

An arrow is red with a speed of 20.0 m/s at a block of Styrofoam resting on a smooth surface. The arrow penetrates a certain distance into the block before coming to rest relative to it. During this process the arrows deceleration has a magnitude of and the blocks acceleration has a magnitude of . (a) How long does it take for the arrow to stop moving with respect to the block? (b) What is the common speed of the arrow and block when this happens? (c) How far into the block does the arrow penetrate?

Sitting in a second-story apartment, a physicist notices a ball moving straight upward just outside her window. The ball is visible for 0.25 s as it moves a distance of 1.05 m from the bottom to the top of the window. (a)How long does it take before the ball reappears? (b) What is the greatest height of the ball above the top of the window?

The Quadratic Formula from Kinematics In this problem we show how the kinematic equations of motion can be used to derive the quadratic formula. First, consider an object with an initial position , an initial velocity , and an acceleration a. To nd the time when this object reaches the position we can use the quadratic formula, or apply the following two-step procedure: (a) Use Equation 212 to show that the velocity of the object when it reaches is given by . (b) Use Equation 27 to show that the time corresponding to the velocity found in part (a) is . (c) To complete our derivation, show that the result of part (b) is the same as applying the quadratic formula to

The rst word spoken on the surface of the Moon after Apollo 15landed on July 30, 1971, was Bam! This was James Irwins involuntary reaction to their rather bone-jarring touchdown. We did hit harder than any of the other ights! says Irwin. And I was startled, obviously, when I said, Bam! The reason for the rm touchdown of Apollo 15, as pilot David Scott later characterized it, was that the rocket engine was shut off a bit earlier than planned, when the lander was still 4.30 ft above the lunar surface and moving downward with a speed of 0.500 ft/s. From that point on the lander descended in lunar free fall, with an acceleration of 1.62 m/s2. As a result, the landing speed of Apollo 15was by far the largest of any of the Apollo missions. In comparison, Neil Armstrongs landing speed on Apollo 11 was the lowest at 1.7 ft/she didnt shut off the engine until the footpads were actually on the surface. Apollos 12, 14, and 17 all landed with speeds between 3.0 and 3.5 ft/s. To better understand the descent of Apollo 15, we show its trajectory during the nal stages of landing in Figure 237(a). In Figure 237 (b) we show a variety of speed-versus-time plots. How long did it take for the lander to drop the nal 4.30 ft to the Moons surface? A. 1.18 s B. 1.37 s C. 1.78 s D. 2.36 s

What was the impact speed of the lander when it touched down? Give your answer in feet per second (ft/s), the same units used by the astronauts. A. 2.41 ft/s B. 6.78 ft/s C. 9.95 ft/s D. 10.6 ft/s

Which of the speed-versus-time plots in Figure 237 (b) correctly represents the speed of the Apollo 15 lander? ABCD

Suppose, instead of shutting off the engine, the astronauts had increased its thrust, giving the lander a small, but constant, upward acceleration. Which speed-versus-time plot in Figure 237 (b) would describe this situation? ABCD

Referring to Example 29 Suppose the speeder (red car) is traveling with a constant speed of 25 m/s, and that the maximum acceleration of the police car (blue car) is . If the police car is to start from rest and catch the speeder in 15 s or less, what is the maximum head-start distance the speeder can have? Measure time from the moment the police car starts.

Referring to Example 29 The speeder passes the position of the police car with a constant speed of 15 m/s. The police car immediately starts from rest and pursues the speeder with constant acceleration. What acceleration must the police car have if it is to catch the speeder in 7.0 s? Measure time from the moment the police car starts.

Referring to Example 212 (a) In Example 212, the bag of sand is released at 20.0 m and reaches a maximum height of 22 m. If the bag had been released at 30.0 m instead, with everything else remaining the same, would its maximum height be 32 m, greater than 32 m, or less than 32 m? (b)Find the speed of the bag just before it lands when it is released from 30.0 m.

Referring to Example 212 Suppose the balloon is descending with a constant speed of 4.2 m/s when the bag of sand comes loose at a height of 35 m. (a) How long is the bag in the air? (b) What is the speed of the bag when it is 15 m above the ground?