Question: The velocity vs. time graph for an

> 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 first stone had an initial velocity of -2.00 m/s. (a) H

> Emily challenges her husband, David, to catch a $1 bill as follows. She holds the bill vertically as in Figure P2.67, with the center of the bill between David’s index finger and thumb. David must catch the bill after Emily releases it

> The thickest and strongest chamber in the human heart is the left ventricle, responsible during systole for pumping oxygenated blood through the aorta to rest of the body. Assume aortic blood starts from rest and accelerates at 22.5 m/s2 to a peak speed

> A ball thrown straight up into the air is found to be moving at 1.50 m/s after rising 2.00 m above its release point. Find the ball’s initial speed.

> A player holds two baseballs a height h above the ground. He throws one ball vertically upward at speed υ0 and the other vertically downward at the same speed. Calculate (a) The speed of each ball as it hits the ground and (b) The difference between thei

> 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?

> An object is moving in the positive direction along the x - axis. Sketch plots of the object’s position vs. time and velocity vs. time if (a) its speed is constant, (b) it’s speeding up at a constant rate, and (c) it’s slowing down at a constant rate.

> An insect called the froghopper (Philaenus spumarius) has been called the best jumper in the animal kingdom. This insect can accelerate at over 4.0 x 103 m/s2 during a displacement of 2.0 mm as it straightens its specially equipped “jumping legs.” (a) As

> Mature salmon swim upstream, returning to spawn at their birthplace. During the arduous trip they leap vertically upward over waterfalls as high as 3.6 m. With what minimum speed must a salmon launch itself into the air to clear a 3.6 - m waterfall?

> Determine which of the following moving objects obey the equations of projectile motion developed in this topic. (a) A ball is thrown in an arbitrary direction. (b) A jet airplane crosses the sky with its engines thrusting the plane forward. (c) A rocket

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

> A speedboat moving at 30.0 m/s approaches a no-wake buoy marker 1.00 x 102 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 veloci

> A bullet is fired through a board 10.0 cm thick in such a way that the bullet’s line of motion is perpendicular to the face of the board. If the initial speed of the bullet is 4.00 x 102 m/s and it emerges from the other side of the board with a speed of

> Colonel John P. Stapp, USAF, participated in studying whether a jet pilot could survive emergency ejection. On March 19, 1954, he rode a rocket- propelled sled that moved down a track at a speed of 632 mi/h (see Fig. P2.56). He and the sled were safely b

> A truck tractor pulls two trailers, one behind the other, at a constant speed of 1.00 x 102 km/h. It takes 0.600 s for the big rig to completely pass onto a bridge 4.00 x 102 m long. For what duration of time is all or part of the truck–trailer combinati

> A baseball is hit so that it travels straight upward after being struck by the bat. A fan observes that it takes 3.00 s for the ball to reach its maximum height. Find (a) The ball’s initial velocity and (b) The height it reaches.

> 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 e

> A package is dropped from a helicopter that is descending steadily at a speed υ0. After t seconds have elapsed, (a) What is the speed of the package in terms of υ0, g, and t? (b) What distance d is it from the helicopter in terms of g and t? (c) What are

> 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 flight? (b) What is the velocity of the ball when it reaches its maximum

> A small mailbag is released from a helicopter that is descending steadily at 1.50 m/s. After 2.00s (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 risin

> If you push on a heavy box that is at rest, you must exert some force to start its motion. Once the box is sliding, why does a smaller force maintain its motion?

> 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 1000 m/s2 lastin

> 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 rock’s speed at the top? If not, what initial s

> A certain freely falling object, released from rest, requires 1.50 s to travel the last 30.0 m before it hits the ground. (a) Find the velocity of the object when it is 30.0 m above the ground. (b) Find the total distance the object travels during the fa

> A ball is thrown directly downward with an initial speed of 8.00 m/s, from a height of 30.0 m. After what time interval does it strike the ground?

> 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 w

> A train 4.00 x 102 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

> 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 first player makes up his mind to chase his opponent. If he accelerates uniformly at 4.0

> The kinematic equations can describe phenomena other than motion through space and time. Suppose x represents a person’s bank account balance. The units of x would be dollars ($), and velocity υ would give the rate at which the balance changes (in units

> 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.

> 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

> A ball is projected horizontally from the top of a building. One second later, another ball is projected horizontally from the same point with the same velocity. (a) At what point in the motion will the balls be closest to each other? (b) Will the first

> 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 b

> 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 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 br

> 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

> 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 y

> 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

> 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 car’s 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 do

> An object moves with constant acceleration 4.00 m/s2 and over a time interval reaches a final velocity of 12.0 m/s. (a) If its original velocity is 6.00 m/s, what is its displacement during the time interval? (b) What is the distance it travels during th

> 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?

> A speedboat increases its speed uniformly from υi = 20.0 m/s to υf = 30.0 m/s in a distance of 2.00 x 102 m. (a) Draw a coordinate system for this situation and label the relevant quantities, including vectors. (b) For the given information, what single

> A space explorer is moving through space far from any planet or star. He notices a large rock, taken as a specimen from an alien planet, floating around the cabin of the ship. Should he push it gently, or should he kick it toward the storage compartment?

> A truck covers 40.0 m in 8.50 s while uniformly slowing down to a final velocity of 2.80 m/s. (a) Find the truck’s original speed. (b) Find its acceleration.

> In 1865 Jules Verne proposed sending men to the Moon by firing a space capsule from a 220-m-long cannon with final speed of 10.97 km/s. What would have been the unrealistically large acceleration experienced by the space travelers during their launch? (A

> An object moving with uniform acceleration has a velocity of 12.0 cm/s in the positive x - direction when its x - coordinate is 3.00 cm. If its x - coordinate 2.00 s later is -5.00 cm, what is its acceleration?

> Solve Example 2.5, “Car Chase,” by a graphical method. On the same graph, plot position versus time for the car and the trooper. From the intersection of the two curves, read the time at which the trooper overtakes the

> 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, find the distance the plane moves.

> If you press a book flat against a vertical wall with your hand, in what direction is the friction force exerted by the wall on the book? (a) Downward (b) Upward (c) Out from the wall (d) Into the wall.

> A small sports car collides head-on with a massive truck. The greater impact force (in magnitude) acts on (a) The car, (b) The truck, (c) Neither, the force is the same on both. Which vehicle undergoes the greater magnitude acceleration? (d) The car, (e)

> Respond to each statement, true or false: (a) No force of gravity acts on an astronaut in an orbiting space station. (b) At three Earth radii from the center of Earth, the acceleration of gravity is one-ninth its surface value. (c) If two identical plane

> Which has greater value, a newton of gold on Earth or a newton of gold on the Moon? (a) The newton of gold on the Earth. (b) The newton of gold on the Moon. (c) The value is the same, regardless.

> Which of the following statements are true? (a) An object can move even when no force acts on it. (b) If an object isn’t moving, no external forces act on it. (c) If a single force acts on an object, the object accelerates. (d) If an object accelerates,

> For the woman being pulled forward on the toboggan in Figure 4.33, is the magnitude of the normal force exerted by the ground on the toboggan (a) Equal to the total weight of the woman plus the toboggan, (b) Greater than the total weight, (c) Less than t

> Consider the two situations shown in Figure 4.30, in which there is no acceleration. In both cases the men pull with a force of magnitude F. Is the reading on the scale in part (i) of the figure (a) Greater than, (b) Less than, or (c) Equal to the readin

> Suppose your friend is sitting on a sled and asks you to move her across a flat, horizontal field. You have a choice of (a) Pushing her from behind by applying a force downward on her shoulders at 30° below the horizontal (Fig. 4.22a) or (b) A

> A crate is sitting in the center of a flatbed truck. As the truck accelerates to the east, the crate moves with it, and doesn’t slide on the bed of the truck. In what direction is the friction force exerted by the bed of the truck on the crate? (a) To th

> As a projectile moves in its parabolic path, where are the velocity and acceleration vectors perpendicular to each other? (a) Everywhere along the projectile’s path (b) At the peak of its path (c) Nowhere along its path (d) Not enough information is give

> Suppose you are carrying a ball and running at constant velocity on level ground. You wish to throw the ball and catch it as it comes back down. Neglecting air resistance, should you (a) Throw the ball at an angle of about 45° above the horizontal and ma

> A certain car is capable of accelerating at a rate of 0.60 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?

> A girl on a bicycle takes 15.0 s to ride halfway around a circular track of radius 10.0 m (Figure 3.4). (a) What is the girl’s average speed? (b) What is the magnitude of her average velocity?

> Consider the following controls in an automobile: gas pedal, brake, steering wheel. The controls in this list that can cause an acceleration of the car are (a) All three controls (b) The gas pedal and the brake (c) Only the brake (d) Only the gas pedal.

> Which of the following objects can’t be accelerating? (a) An object moving with a constant speed (b) An object moving with a constant velocity or (c) An object moving along a curve.

> A woman at an airport is towing her 20.0-kg suitcase at constant speed by pulling on a strap at an angle u above the horizontal (Fig. 4.76). She pulls on the strap with a 35.0-N force, and the friction force on the suitcase is 20.0 N. (a) Draw a free-bod

> (a) What is the resultant force exerted by the two cables supporting the traffic light in Figure P4.75? (b) What is the weight of the light? Figure P4.75:

> (a) What is the minimum force of friction required to hold the system of Figure P4.74 in equilibrium? (b) What coefficient of static friction between the 100.-N block and the table ensures equilibrium? (c) If the coefficient of kinetic friction between t

> Three objects are connected on a table as shown in Figure P4.73. The coefficient of kinetic friction between the block of mass m2 and the table is 0.350. The objects have masses of m1 = 4.00 kg, m2 = 1.00 kg, and m3 = 2.00 kg as shown, and the pulleys ar

> As a protest against the umpire’s calls, a baseball pitcher throws a ball straight up into the air at a speed of 20.0 m/s. In the process, he moves his hand through a distance of 1.50 m. If the ball has a mass of 0.150 kg, find the force he exerts on the

> Two blocks each of mass m = 3.50 kg are fastened to the top of an elevator as in Figure P4.56. (a) If the elevator has an upward acceleration a = 1.60 m/s2, find the tensions T1 and T2 in the upper and lower strings. (b) If the strings can withstand a ma

> Objects of masses m1 = 4.00 kg and m2 = 9.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.70. The object m1 is held at rest on the floor, and m2 rests on a fixed incline of θ = 40.0°. T

> The average person passes out at an acceleration of 7g (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

> A 15.0-lb block rests on a horizontal floor. (a) What force does the floor exert on the block? (b) A rope is tied to the block and is run vertically over a pulley. The other end is attached to a free-hanging 10.0-lb object. What now is the force exerted

> A block of mass 3m is placed on a frictionless horizontal surface, and a second block of mass m is placed on top of the first block. The surfaces of the blocks are rough. A constant force of magnitude F is applied to the first block as in Figure P4.68. (

> In Figure P4.64, m1 = 10. kg and m2 = 4.0 kg. The coefficient of static friction between m1 and the horizontal surface is 0.50, and the coefficient of kinetic friction is 0.30. (a) If the system is released from rest, what will its acceleration be? (b) I

> Two objects with masses of 3.00 kg and 5.00 kg are connected by a light string that passes over a frictionless pulley, as in Figure P4.66. Determine (a) The tension in the string, (b) The acceleration of each object, and (c) The distance each object will

> Objects with masses m1 = 10.0 kg and m2 = 5.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.64. If, when the system starts from rest, m2 falls 1.00 m in 1.20 s, determine the coefficient of kinetic friction be

> An object with mass m1 = 5.00 kg rests on a frictionless horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass m2 = 10.0 kg, as shown in Figure P4.64. Find (a) The acceleration of each o

> In Figure P4.63, the light, taut, unstretchable cord B joins block 1 and the larger-mass block 2. Cord A exerts a force on block 1 to make it accelerate forward. (a) How does the magnitude of the force exerted by cord A on block 1 compare with the magnit

> Two blocks of masses m1 and m2 (m1 > m2) are placed on a frictionless table in contact with each other. A horizontal force of magnitude F is applied to the block of mass m1 in Figure P4.62. (a) If P is the magnitude of the contact force between the bl

> A 1.00 x 103 car is pulling a 300.-kg trailer. Together, the car and trailer have an acceleration of 2.15 m/s2 in the positive x - direction. Neglecting frictional forces on the trailer, determine (a) The net force on the car, (b) The net force on the tr

> Two packing crates of masses 10.0 kg and 5.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.60. The 5.00-kg crate lies on a smooth incline of angle 40.0°. Find (a) The acceleration of the 5.00-kg cra

> A 50.0-g Super Ball traveling at 25.0 m/s bounces off a brick wall and rebounds at 22.0 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.50 ms, what is the magnitude of the average acceleration of the ball during

> The determined Wile E. Coyote is out once more to try to capture the elusive roadrunner. The coyote wears a new pair of power roller skates, which provide a constant horizontal acceleration of 15.0 m/s2, as shown in Figure P3.59. The coyote starts off at

> A football receiver running straight downfield at 5.50 m/s is 10.0 m in front of the quarterback when a pass is thrown downfield at 25.0° above the horizon (Fig. P3.58). If the receiver never changes speed and the ball is caught at the same he

> One strategy in a snowball fight is to throw a snowball at a high angle over level ground. Then, while your opponent is watching that snowball, you throw a second one at a low angle timed to arrive before or at the same time as the first one. Assume both

> Antlion larvae lie in wait for prey at the bottom of a conical pit about 5.0 cm deep and 3.8 cm in radius. When a small insect ventures into the pit, it slides to the bottom and is seized by the antlion. If the prey attempts to escape, the antlion rapidl

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

> A landscape architect is planning an artificial waterfall in a city park. Water flowing at 0.750 m/s leaves the end of a horizontal channel at the top of a vertical wall h = 2.35 m high and falls into a pool (Fig. P3.54). (a) How far from the wall will

> A celebrated Mark Twain story has motivated contestants in the Calaveras County Jumping Frog Jubilee, where frog jumps as long as 2.2 m have been recorded. If a frog jumps 2.2 m and the launch angle is 45°, find (a) The frog’s launch speed (b) The time

> If raindrops are falling vertically at 7.50 m/s, what angle from the vertical do they make for a person jogging at 2.25 m/s?

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

> Chinook salmon are able to move upstream faster by jumping out of the water periodically; this behaviour is called porpoising. Suppose a salmon swimming in still water jumps out of the water with a speed of 6.26 m/s at an angle of 45°, sails through the

> A particle starts from rest and accelerates as shown in Figure P2.20. Determine (a) The particle’s speed at t = 10.0 s and at t = 20.0 s, and (b) The distance traveled in the first 20.0 s.

> Construct motion diagrams showing the velocity and acceleration of a projectile at several points along its path, assuming (a) The projectile is launched horizontally (b) The projectile is launched at an angle θ with the horizontal.

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

> When baseball outfielders throw the ball, they usually allow it to take one bounce, on the theory that the ball arrives at its target sooner that way. Suppose that, after the bounce, the ball rebounds at the same angle θ that it had when it

> Spitting cobras can defend themselves by squeezing muscles around their venom glands to squirt venom at an attacker. Suppose a spitting cobra rears up to a height of 0.500 m above the ground and launches venom at 3.50 m/s, directed 50.0° above the horizo

> The x - and y - coordinates of a projectile launched from the origin are x = υ0xt and y = υ0yt – 1/2 gt2. Solve the first of these equations for time t and substitute into the second to show that the path of a projectile is a parabola with the form y = a

> A quarterback throws a football toward a receiver with an initial speed of 20. m/s at an angle of 30° above the horizontal. At that instant the receiver is 20. m from the quarterback. In (a) What direction and (b) With what constant speed should the rece

> A 2.00-m-tall basketball player is standing on the floor 10.0 m from the basket, as in Figure P3.44. If he shoots the ball at a 40.0° angle with the horizontal, at what initial speed must he throw the basketball so that it goes through the hoo