The graphical solution corresponds to fi nding the

Does a doubling of an objects average speed always double the magnitude of its displacement in a given amount of time? Explain.

Would a vertical line in a graph of position versus time make sense? Explain.

Can the tangent line to a velocity vs. time graph ever be vertical? Explain.

What is the fi nal speed if the displacement is increased by a factor of 4?

The graphical solution corresponds to fi nding the intersection of what two types of curves in the xt-plane?

How would the answer change if the plane coasted for 2.0 s before the pilot applied the brakes?

According to the graph in Figure 2.19a, at what different times is the acceleration zero?

How would the answer to part (b), the maximum height, change if the person throwing the ball jumped upward at the instant he released the ball?

By what factor would the maximum displacement above the rooftop be increased if the building were transported to the Moon, where a 5 21 6g ?

If, instead, some fuel remains, at what height should the engines be fi red again to brake the rockets fall and allow a perfectly soft landing? (Assume the same acceleration as during the initial ascent.)

An arrow is shot straight up in the air at an initial speed of 15.0 m/s. After how much time is the arrow heading downward at a speed of 8.00 m/s? (a) 0.714 s (b) 1.24 s (c) 1.87 s (d) 2.35 s (e) 3.22 s

A cannon shell is fi red straight up in the air at an initial speed of 225 m/s. After how much time is the shell at a height of 6.20  102 m and heading down? (a) 2.96 s (b) 17.3 s (c) 25.4 s (d) 33.6 s (e) 43.0 s

When applying the equations of kinematics for an object moving in one dimension, which of the following statements must be true? (a) The velocity of the object must remain constant. (b) The acceleration of the object must remain constant. (c) The velocity of the object must increase with time. (d) The position of the object must increase with time. (e) The velocity of the object must always be in the same direction as its acceleration.

A juggler throws a bowling pin straight up in the air. After the pin leaves his hand and while it is in the air, which statement is true? (a) The velocity of the pin is always in the same direction as its acceleration. (b) The velocity of the pin is never in the same direction as its acceleration. (c) The acceleration of the pin is zero. (d) The velocity of the pin is opposite its acceleration on the way up. (e) The velocity of the pin is in the same direction as its acceleration on the way up.

A racing car starts from rest and reaches a fi nal speed v in a time t. If the acceleration of the car is constant during this time, which of the following statements must be true? (a) The car travels a distance vt. (b) The average speed of the car is v/2. (c) The acceleration of the car is v/t. (d) The velocity of the car remains constant. (e) None of these

A pebble is dropped from rest from the top of a tall cliff and falls 4.9 m after 1.0 s has elapsed. How much farther does it drop in the next 2.0 seconds? (a) 9.8 m (b) 19.6 m (c) 39 m (d) 44 m (e) 27 m

An object moves along the x-axis, its position measured at each instant of time. The data are organized into an accurate graph of x vs. t. Which of the following quantities cannot be obtained from this graph? (a) the velocity at any instant (b) the acceleration at any instant (c) the displacement during some time interval (d) the average velocity during some time interval (e) the speed of the particle at any instant

People become uncomfortable in an elevator if it accelerates from rest at a rate such that it attains a speed of about 6 m/s after descending ten stories (about 30 m). What is the approximate magnitude of its acceleration? (Choose the closest answer.) (a) 10 m/s2 (b) 0.3 m/s2 (c) 0.6 m/s2 (d) 1 m/s2 (e) 0.8 m/s2

Races are timed to an accuracy of 1/1 000 of a second. What distance could a person rollerblading at a speed of 8.5 m/s travel in that period of time? (a) 85 mm (b) 85 cm (c) 8.5 m (d) 8.5 mm (e) 8.5 km

A student at the top of a building throws a red ball upward with speed v0 and then throws a blue ball downward with the same initial speed v0. Immediately before the two balls reach the ground, which of the following statements are true? (Choose all correct statements; neglect air friction.) (a) The speed of the red ball is less than that of the blue ball. (b) The speed of the red ball is greater than that of the blue ball. (c) Their velocities are equal. (d) The speed of each ball is greater than v0. (e) The acceleration of the blue ball is greater than that of the red ball.

A rock is thrown downward from the top of a 40.0 m tower with an initial speed of 12 m/s. Assuming negligible air resistance, what is the speed of the rock just before hitting the ground? (a) 28 m/s (b) 30 m/s (c) 56 m/s (d) 784 m/s (e) More information is needed.

A ball is thrown straight up in the air. For which situation are both the instantaneous velocity and the acceleration zero? (a) on the way up (b) at the top of the fl ight path (c) on the way down (d) halfway up and halfway down (e) none of these

If the velocity of a particle is nonzero, can the particles acceleration be zero? Explain

If the velocity of a particle is zero, can the particles acceleration be zero? Explain

. If a car is traveling eastward, can its acceleration be westward? Explain.

Can the equations of kinematics be used in a situation where the acceleration varies with time? Can they be used when the acceleration is zero?

If the average velocity of an object is zero in some time interval, what can you say about the displacement of the object during that interval?

Figure CQ2.6 shows strobe photographs taken of a disk moving from left to right under different conditions. The time interval between images is constant. Taking the direction to the right to be positive, describe the motion of the disk in each case. For which case is (a) the accel er ation positive? (b) the acceleration negative? (c) the velocity constant?

Can the instantaneous velocity of an object at an instant of time ever be greater in magnitude than the average velocity over a time interval containing that instant? Can it ever be less?

A ball is thrown straight up in the air. For which situation are both the instantaneous velocity and the acceleration zero? (a) on the way up (b) at the top of the fl ight path (c) on the way down (d) halfway up and halfway down (e) none of these

Consider the following combinations of signs and values for the velocity and acceleration of a particle with respect to a one-dimensional x-axis: Velocity Acceleration a. Positive Positive b. Positive Negative c. Positive Zero d. Negative Positive e. Negative Negative f. Negative Zero g. Zero Positive h. Zero Negative Describe what the particle is doing in each case and give a real-life example for an automobile on an east west one- dimensional axis, with east considered the positive direction.

A ball rolls in a straight line along the horizontal direction. Using motion diagrams (or multifl ash photographs), describe the velocity and acceleration of the ball for each of the following situations: (a) The ball moves to the right at a constant speed. (b) The ball moves from right to left and continually slows down. (c) The ball moves from right to left and continually speeds up. (d) The ball moves to the right, fi rst speeding up at a constant rate and then slowing down at a constant rate.

The speed of a nerve impulse in the human body is about 100 m/s. If you accidentally stub your toe in the dark, estimate the time it takes the nerve impulse to travel to your brain.

Light travels at a speed of about 3  108 m/s. How many miles does a pulse of light travel in a time interval of 0.1 s, which is about the blink of an eye? Compare this distance to the diameter of Earth.

A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 30.0 min at 80.0 km/h, 12.0 min at 100 km/h, and 45.0 min at 40.0 km/h and spends 15.0 min eating lunch and buying gas. (a) Determine the average speed for the trip. (b) Determine the distance between the initial and fi nal cities along the route.

(a) Sand dunes on a desert island move as sand is swept up the windward side to settle in the leeward side. Such walking dunes have been known to travel 20 feet in a year and can travel as much as 100 feet per year in particularly windy times. Calculate the average speed in each case in meters per second. (b) Fingernails grow at the rate of drifting continents, about 10 mm/yr. Approximately how long did it take for North America to separate from Europe, a distance of about 3 000 mi?

Two boats start together and race across a 60-km-wide lake and back. Boat A goes across at 60 km/h and returns at 60 km/h. Boat B goes across at 30 km/h, and its crew, realizing how far behind it is getting, returns at 90 km/h. Turnaround times are negligible, and the boat that completes the round trip fi rst wins. (a) Which boat wins and by how much? (Or is it a tie?) (b) What is the average velocity of the winning boat?

A graph of position versus time for a certain particle moving along the x-axis is shown in Figure P2.6. Find the average velocity in the time intervals from (a) 0 to 2.00 s, (b) 0 to 4.00 s, (c) 2.00 s to 4.00 s, (d) 4.00 s to 7.00 s, and (e) 0 to 8.00 s.

A motorist drives north for 35.0 minutes at 85.0 km/h and then stops for 15.0 minutes. He then continues north, traveling 130 km in 2.00 h. (a) What is his total displacement? (b) What is his average velocity?

A tennis player moves in a straight-line path as shown in Figure P2.8. Find her average velocity in the time intervals from (a) 0 to 1.0 s, (b) 0 to 4.0 s, (c) 1.0 s to 5.0 s, and (d) 0 to 5.0 s.

Find the instantaneous velocities of the tennis player of Figure P2.8 at (a) 0.50 s, (b) 2.0 s, (c) 3.0 s, and (d) 4.5 s.

Two cars travel in the same direction along a straight highway, one at a constant speed of 55 mi/h and the other at 70 mi/h. (a) Assuming they start at the same point, how much sooner does the faster car arrive at a destination 10 mi away? (b) How far must the faster car travel before it has a 15-min lead on the slower car?

If the average speed of an orbiting space shuttle is 19 800 mi/h, determine the time required for it to circle Earth. Make sure you consider that the shuttle is orbiting about 2.00  102 mi above Earths surface and assume that Earths radius is 3 963 miles.

An athlete swims the length L of a pool in a time t1 and makes the return trip to the starting position in a time t2. If she is swimming initially in the positive xdirection, determine her average velocities symbolically in (a) the fi rst half of the swim, (b) the second half of the swim, and (c) the round trip. (d) What is her average speed for the round trip?

. A person takes a trip, driving with a constant speed of 89.5 km/h, except for a 22.0-min rest stop. If the persons average speed is 77.8 km/h, how much time is spent on the trip and how far does the person travel?

A tortoise can run with a speed of 0.10 m/s, and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 2.0 minutes. The tortoise wins by a shell (20 cm). (a) How long does the race take? (b) What is the length of the race?

To qualify for the fi nals in a racing event, a race car must achieve an average speed of 250 km/h on a track with a total length of 1 600 m. If a particular car covers the fi rst half of the track at an average speed of 230 km/h, what minimum average speed must it have in the second half of the event in order to qualify?

One athlete in a race running on a long, straight track with a constant speed v1 is a distance d behind a second athlete running with a constant speed v2. (a) Under what circumstances is the fi rst athlete able to overtake the second athlete? (b) Find the time t it takes the fi rst athlete to overtake the second athlete, in terms of d, v1, and v2. (c) At what minimum distance d2 from the leading athlete must the fi nish line be located so that the trailing athlete can at least tie for fi rst place? Express d2 in terms of d, v1, and v2 by using the result of part (b).

. A graph of position versus time for a certain particle moving along the x-axis is shown in Figure P2.6. Find the instantaneous velocity at the instants (a) t  1.00 s, (b) t  3.00 s, (c) t  4.50 s, and (d) t  7.50 s.

A race car moves such that its position fi ts the relationship x  (5.0 m/s)t  (0.75 m/s3)t 3 where x is measured in meters and t in seconds. (a) Plot a graph of the cars position versus time. (b) Determine the instantaneous velocity of the car at t  4.0 s, using time intervals of 0.40 s, 0.20 s, and 0.10 s. (c) Compare the average velocity during the fi rst 4.0 s with the results of part (b).

Runner A is initially 4.0 mi west of a fl agpole and is running with a constant velocity of 6.0 mi/h due east. Runner B is initially 3.0 mi east of the fl agpole and is running with a constant velocity of 5.0 mi/h due west. How far are the runners from the fl agpole when they meet?

Assume a canister in a straight tube moves with a constant acceleration of 4.00 m/s2 and has a velocity of 13.0 m/s at t  0. (a) What is its velocity at t  1.00 s? (b) At t  2.00 s? (c) At t  2.50 s? (d) At t  4.00 s? (e) Describe the shape of the canisters velocity versus time graph. (f) What two things must be known at a given time to predict the canisters velocity at any later time?

Secretariat ran the Kentucky Derby with times of 25.2 s, 24.0 s, 23.8 s, 23.2 s, and 23.0 s for the quarter mile. (a) Find his average speed during each quarter-mile segment in ft/s. (b) Assuming that Secretariats instantaneous speed at the fi nish line was the same as his average speed during the fi nal quarter mile, fi nd his average acceleration for the entire race in ft/s2. (Hint: Recall that horses in the Derby start from rest.)

The average person passes out at an acceleration of 7 g (that is, seven times the gravitational acceleration on Earth). Suppose a car is designed to accelerate at this rate. How much time would be required for the car to accelerate from rest to 60.0 miles per hour? (The car would need rocket boosters!)

A certain car is capable of accelerating at a rate of 10.60 m/s2. How long does it take for this car to go from a speed of 55 mi/h to a speed of 60 mi/h?

The velocity vs. time graph for an object moving along a straight path is shown in Figure P2.24. (a) Find the average acceleration of the object during the time intervals 0 to 5.0 s, 5.0 s to 15 s, and 0 to 20 s. (b) Find the instantaneous acceleration at 2.0 s, 10 s, and 18 s.

A steam catapult launches a jet aircraft from the aircraft carrier John C. Stennis, giving it a speed of 175 mi/h in 2.50 s. (a) Find the average acceleration of the plane. (b) Assuming the acceleration is constant, fi nd the distance the plane moves.

A car is traveling due east at 25.0 m/s at some instant. (a) If its constant acceleration is 0.750 m/s2 due east, fi nd its velocity after 8.50 s have elapsed. (b) If its constant acceleration is 0.750 m/s2 due west, fi nd its velocity after 8.50 s have elapsed.

A car traveling east at 40.0 m/s passes a trooper hiding at the roadside. The driver uniformly reduces his speed to 25.0 m/s in 3.50 s. (a) What is the magnitude and direction of the cars acceleration as it slows down? (b) How far does the car travel in the 3.5-s time period?

In 1865 Jules Verne proposed sending men to the Moon by fi ring a space capsule from a 220-m-long cannon with fi nal speed of 10.97 km/s. What would have been the unrealistically large acceleration experienced by the space travelers during their launch? (A human can stand an acceleration of 15g for a short time.) Compare your answer with the free-fall acceleration, 9.80 m/s2.

A truck covers 40.0 m in 8.50 s while smoothly slowing down to a fi nal velocity of 2.80 m/s. (a) Find the trucks original speed. (b) Find its acceleration.

A speedboat increases its speed uniformly from vi  20.0 m/s to vf  30.0 m/s in a distance of 2.00  102 m. (a) Draw a coordinate system for this situation and label the relevant quantities, including vectors. (b) For the given information, what single equation is most appropriate for fi nding the acceleration? (c) Solve the equation selected in part (b) symbolically for the boats acceleration in terms of vf , va, and x. (d) Substitute given values, obtaining that acceleration. (e) Find the time it takes the boat to travel the given distance.

A Cessna aircraft has a liftoff speed of 120 km/h. (a) What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of 240 m? (b) How long does it take the aircraft to become airborne?

Problems 51 truck travels for 20 s at constant speed until the brakes are applied, stopping the truck in a uniform manner in an additional 5.0 s. (a) How long is the truck in motion? (b) What is the average velocity of the truck during the motion described?

In a test run, a certain car accelerates uniformly from zero to 24.0 m/s in 2.95 s. (a) What is the magnitude of the cars acceleration? (b) How long does it take the car to change its speed from 10.0 m/s to 20.0 m/s? (c) Will doubling the time always double the change in speed? Why?

A jet plane lands with a speed of 100 m/s and can accelerate at a maximum rate of 5.00 m/s2 as it comes to rest. (a) From the instant the plane touches the runway, what is the minimum time needed before it can come to rest? (b) Can this plane land on a small tropical island airport where the runway is 0.800 km long?

Speedy Sue, driving at 30.0 m/s, enters a one-lane tunnel. She then observes a slow-moving van 155 m ahead traveling at 5.00 m/s. Sue applies her brakes but can accelerate only at 2.00 m/s2 because the road is wet. Will there be a collision? State how you decide. If yes, determine how far into the tunnel and at what time the collision occurs. If no, determine the distance of closest approach between Sues car and the van.

A record of travel along a straight path is as follows: 1. Start from rest with a constant acceleration of 2.77 m/s2 for 15.0 s. 2. Maintain a constant velocity for the next 2.05 min. 3. Apply a constant negative acceleration of 9.47 m/s2 for 4.39 s. (a) What was the total displacement for the trip? (b) What were the average speeds for legs 1, 2, and 3 of the trip, as well as for the complete trip?

A train is traveling down a straight track at 20 m/s when the engineer applies the brakes, resulting in an acceleration of 1.0 m/s2 as long as the train is in motion. How far does the train move during a 40-s time interval starting at the instant the brakes are applied?

. A car accelerates uniformly from rest to a speed of 40.0 mi/h in 12.0 s. Find (a) the distance the car travels during this time and (b) the constant acceleration of the car.

A car starts from rest and travels for 5.0 s with a uniform acceleration of 1.5 m/s2. The driver then applies the brakes, causing a uniform acceleration of 2.0 m/s2. If the brakes are applied for 3.0 s, (a) how fast is the car going at the end of the braking period, and (b) how far has the car gone?

A car starts from rest and travels for t1 seconds with a uniform acceleration a1. The driver then applies the brakes, causing a uniform acceleration a2. If the brakes are applied for t2 seconds, (a) how fast is the car going just before the beginning of the braking period? (b) How far does the car go before the driver begins to brake? (c) Using the answers to parts (a) and (b) as the initial velocity and position for the motion of the car during braking, what total distance does the car travel? Answers are in terms of the variables a1, a2, t1, and t2.

In the Daytona 500 auto race, a Ford Thunderbird and a Mercedes Benz are moving side by side down a straightaway at 71.5 m/s. The driver of the Thunderbird realizes that she must make a pit stop, and she smoothly slows to a stop over a distance of 250 m. She spends 5.00 s in the pit and then accelerates out, reaching her previous speed of 71.5 m/s after a distance of 350 m. At this point, how far has the Thunderbird fallen behind the Mercedes Benz, which has continued at a constant speed?

A certain cable car in San Francisco can stop in 10 s when traveling at maximum speed. On one occasion, the driver sees a dog a distance d m in front of the car and slams on the brakes instantly. The car reaches the dog 8.0 s later, and the dog jumps off the track just in time. If the car travels 4.0 m beyond the position of the dog before coming to a stop, how far was the car from the dog? (Hint: You will need three equations.)

A hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of 12 m/s, skates by with the puck. After 3.0 s, the fi rst player makes up his mind to chase his opponent. If he accelerates uniformly at 4.0 m/s2, (a) how long does it take him to catch his opponent, and (b) how far has he traveled in that time? (Assume the player with the puck remains in motion at constant speed.)

A train 400 m long is moving on a straight track with a speed of 82.4 km/h. The engineer applies the brakes at a crossing, and later the last car passes the crossing with a speed of 16.4 km/h. Assuming constant acceleration, determine how long the train blocked the crossing. Disregard the width of the crossing.

A ball is thrown vertically upward with a speed of 25.0 m/s. (a) How high does it rise? (b) How long does it take to reach its highest point? (c) How long does the ball take to hit the ground after it reaches its highest point? (d) What is its velocity when it returns to the level from which it started?

It is possible to shoot an arrow at a speed as high as 100 m/s. (a) If friction is neglected, how high would an arrow launched at this speed rise if shot straight up? (b) How long would the arrow be in the air?

A certain freely falling object requires 1.50 s to travel the last 30.0 m before it hits the ground. From what height above the ground did it fall?

An attacker at the base of a castle wall 3.65 m high throws a rock straight up with speed 7.40 m/s at a height of 1.55 m above the ground. (a) Will the rock reach the top of the wall? (b) If so, what is the rocks speed at the top? If not, what initial speed must the rock have to reach the top? (c) Find the change in the speed of a rock thrown straight down from the top of the wall at an initial speed of 7.40 m/s and moving between the same two points. (d) Does the change in speed of the downward-moving rock agree with the magnitude of the speed change of the rock moving upward between the same elevations? Explain physically why or why not.

Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 m/s2 lasting for any length of time will not cause injury, whereas an acceleration greater than 1 000 m/s2 lasting for at least 1 ms will cause injury. Suppose a small child rolls off a bed that is 0.40 m above the fl oor. If the fl oor is hardwood, the childs head is brought to rest in approximately 2.0 mm. If the fl oor is carpeted, this stopping distance is increased to about 1.0 cm. Calculate the magnitude and duration of the deceleration in both cases, to determine the risk of injury. Assume the child remains horizontal during the fall to the fl oor. Note that a more complicated fall could result in a head velocity greater or less than the speed you calculate

A small mailbag is released from a helicopter that is descending steadily at 1.50 m/s. After 2.00 s, (a) what is the speed of the mailbag, and (b) how far is it below the helicopter? (c) What are your answers to parts (a) and (b) if the helicopter is rising steadily at 1.50 m/s?

A tennis player tosses a tennis ball straight up and then catches it after 2.00 s at the same height as the point of release. (a) What is the acceleration of the ball while it is in fl ight? (b) What is the velocity of the ball when it reaches its maximum height? Find (c) the initial velocity of the ball and (d) the maximum height it reaches.

A package is dropped from a helicopter that is descending steadily at a speed v0. After t seconds have elapsed, (a) what is the speed of the package in terms of v0, g, and t? (b) What distance d is it from the helicopter in terms of g and t? (c) What are the answers to parts (a) and (b) if the helicopter is rising steadily at the same speed?

A model rocket is launched straight upward with an initial speed of 50.0 m/s. It accelerates with a constant upward acceleration of 2.00 m/s2 until its engines stop at an altitude of 150 m. (a) What can you say about the motion of the rocket after its engines stop? (b) What is the maximum height reached by the rocket? (c) How long after liftoff does the rocket reach its maximum height? (d) How long is the rocket in the air?

. A parachutist with a camera descends in free fall at a speed of 10 m/s. The parachutist releases the camera at an altitude of 50 m. (a) How long does it take the camera to reach the ground? (b) What is the velocity of the camera just before it hits the ground?

. A truck tractor pulls two trailers, one behind the other, at a constant speed of 100 km/h. It takes 0.600 s for the big rig to completely pass onto a bridge 400 m long. For what duration of time is all or part of the trucktrailer combination on the bridge?

A speedboat moving at 30.0 m/s approaches a no-wake buoy marker 100 m ahead. The pilot slows the boat with a constant acceleration of 3.50 m/s2 by reducing the throttle. (a) How long does it take the boat to reach the buoy? (b) What is the velocity of the boat when it reaches the buoy?

A bullet is fi red through a board 10.0 cm thick in such a way that the bullets line of motion is perpendicular to the face of the board. If the initial speed of the bullet is 400 m/s and it emerges from the other side of the board with a speed of 300 m/s, fi nd (a) the acceleration of the bullet as it passes through the board and (b) the total time the bullet is in contact with the board.

An indestructible bullet 2.00 cm long is fi red straight through a board that is 10.0 cm thick. The bullet strikes the board with a speed of 420 m/s and emerges with a speed of 280 m/s. (a) What is the average acceleration of the bullet through the board? (b) What is the total time that the bullet is in contact with the board? (c) What thickness of board (calculated to 0.1 cm) would it take to stop the bullet, assuming the acceleration through all boards is the same?

A student throws a set of keys vertically upward to his fraternity brother, who is in a window 4.00 m above. The brothers outstretched hand catches the keys 1.50 s later. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught?

A student throws a set of keys vertically upward to his fraternity brother, who is in a window a distance h above. The brothers outstretched hand catches the keys on their way up a time t later. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught? (Answers should be in terms of h, g, and t.)

It has been claimed that an insect called the froghopper (Philaenus spumarius) is the best jumper in the animal kingdom. This insect can accelerate at 4 000 m/s2 over a distance of 2.0 mm as it straightens its specially designed jumping legs. (a) Assuming a uniform acceleration, what is the velocity of the insect after it has accelerated through this short distance, and how long did it take to reach that velocity? (b) How high would the insect jump if air resistance could be ignored? Note that the actual height obtained is about 0.7 m, so air resistance is important here.

A ranger in a national park is driving at 35.0 mi/h when a deer jumps into the road 200 ft ahead of the vehicle. After a reaction time t, the ranger applies the brakes to produce an acceleration a  9.00 ft/s2. What is the maximum reaction time allowed if she is to avoid hitting the deer?

A ball is thrown upward from the ground with an initial speed of 25 m/s; at the same instant, another ball is dropped from a building 15 m high. After how long will the balls be at the same height?

To pass a physical education class at a university, a student must run 1.0 mi in 12 min. After running for 10 min, she still has 500 yd to go. If her maximum acceleration is 0.15 m/s2, can she make it? If the answer is no, determine what acceleration she would need to be successful.

Two students are on a balcony 19.6 m above the street. One student throws a ball vertically downward at 14.7 m/s; at the same instant, the other student throws a ball vertically upward at the same speed. The second ball just misses the balcony on the way down. (a) What is the difference in the two balls time in the air? (b) What is the velocity of each ball as it strikes the ground? (c) How far apart are the balls 0.800 s after they are thrown?

Two students are on a balcony a distance h above the street. One student throws a ball vertically downward at a speed v0; at the same time, the other student throws a ball vertically upward at the same speed. Answer the following symbolically in terms of v0, g, h, and t. (a) Write the kinematic equation for the y-coordinate of each ball. (b) Set the equations found in part (a) equal to height 0 and solve each for t symbolically using the quadratic formula. What is the difference in the two balls time in the air? (c) Use the time-independent kinematics equation to fi nd the velocity of each ball as it strikes the ground. (d) How far apart are the balls at a time t after they are released and before they strike the ground?

. You drop a ball from a window on an upper fl oor of a building and it is caught by a friend on the ground when the ball is moving with speed vf . You now repeat the drop, but you have a friend on the street below throw another ball upward at speed vf exactly at the same time that you drop your ball from the window. The two balls are initially separated by 28.7 m. (a) At what time do they pass each other? (b) At what location do they pass each other relative the window?

. The driver of a truck slams on the brakes when he sees a tree blocking the road. The truck slows down uniformly with an acceleration of 5.60 m/s2 for 4.20 s, making skid marks 62.4 m long that end at the tree. With what speed does the truck then strike the tree?

Emily challenges her husband, David, to catch a $1 bill as follows. She holds the bill vertically as in Figure P2.69, with the center of the bill between Davids index fi nger and thumb. David must catch the bill after Emily releases it without moving his hand downward. If his reaction time is 0.2 s, will he succeed? Explain your reasoning. (This challenge is a good trick you might want to try with your friends.)

A mountain climber stands at the top of a 50.0-m cliff that overhangs a calm pool of water. She throws two stones vertically downward 1.00 s apart and observes that they cause a single splash. The fi rst stone had an initial velocity of 2.00 m/s. (a) How long after release of the fi rst stone did the two stones hit the water? (b) What initial velocity must the second stone have had, given that they hit the water simultaneously? (c) What was the velocity of each stone at the instant it hit the water?

An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at 40 ft/s2. After some time t1, the rocket engine is shut down and the sled moves with constant velocity v for a time t2. If the total distance traveled by the sled is 17 500 ft and the total time is 90 s, fi nd (a) the times t1 and t2 and (b) the velocity v. At the 17 500-ft mark, the sled begins to accelerate at 20 ft/s2. (c) What is the fi nal position of the sled when it comes to rest? (d) How long does it take to come to rest?

In Bosnia, the ultimate test of a young mans courage used to be to jump off a 400-year-old bridge (now destroyed) into the River Neretva, 23 m below the bridge. (a) How long did the jump last? (b) How fast was the jumper traveling upon impact with the river? (c) If the speed of sound in air is 340 m/s, how long after the jumper took off did a spectator on the bridge hear the splash?

A person sees a lightning bolt pass close to an airplane that is fl ying in the distance. The person hears thunder 5.0 s after seeing the bolt and sees the airplane overhead 10 s after hearing the thunder. The speed of sound in air is 1 100 ft/s. (a) Find the distance of the airplane from the person at the instant of the bolt. (Neglect the time it takes the light to travel from the bolt to the eye.) (b) Assuming the plane travels with a constant speed toward the person, fi nd the velocity of the airplane. (c) Look up the speed of light in air and defend the approximation used in part (a).

A glider on an air track carries a fl ag of length through a stationary photogate, which measures the time interval td during which the fl ag blocks a beam of infrared light passing across the photogate. The ratio vd  /td is the average velocity of the glider over this part of its motion. Suppose the glider moves with constant acceleration. (a) Is vd necessarily equal to the instantaneous velocity of the glider when it is halfway through the photogate in space? Explain. (b) Is vd equal to the instantaneous velocity of the glider when it is halfway through the photogate in time? Explain. 75.

A stuntman sitting on a tree limb wishes to drop vertically onto a horse galloping under the tree. The constant speed of the horse is 10.0 m/s, and the man is initially 3.00 m above the level of the saddle. (a) What must be the horizontal distance between the saddle and the limb when the man makes his move? (b) How long is he in the air?