Answer: Most of us know intuitively that in a head-on

A soccer player runs up behind a 0.450-kg soccer ball traveling at 3.20 m/s and kicks it in the same direction as it is moving, increasing its speed to 12.8 m/s. What magnitude impulse did the soccer player deliver to the ball? (a) 2.45 kg ? m/s (b) 4.32 kg ? m/s (c) 5.61 kg ? m/s (d) 7.08 kg ? m/s (e) 9.79 kg ? m/s

A small china bowl having kinetic energy E is sliding along a frictionless countertop when a server, with perfect timing, places a rice ball into the bowl as it passes him. If the bowl and rice ball have the same mass, what is the kinetic energy of the system thereafter? (a) 2E (b) E (c) E/2 (d) E/4 (e) E/8

A car of mass m traveling at speed v crashes into the rear of a truck of mass 2m that is at rest and in neutral at an intersection. If the collision is perfectly inelastic, what is the speed of the combined car and truck after the collision? (a) v (b) v/2 (c) v/3 (d) 2v (e) None of these

A 57.0-g tennis ball is traveling straight at a player at 21.0 m/s. The player volleys the ball straight back at 25.0 m/s. If the ball remains in contact with the racket for 0.060 s, what average force acts on the ball? (a) 22.6 kg ? m/s2 (b) 32.5 kg ? m/s2 (c) 43.7 kg ? m/s2 (d) 72.1 kg ? m/s2 (e) 102 kg ? m/s2

In a game of billiards, a red billiard ball is traveling in the positive x-direction with speed v and the cue ball is traveling in the negative x-direction with speed 3v when the two balls collide head on. Which statement is true concerning their velocities subsequent to the collision? Neglect any effects of spin. (a) red ball: 2v; cue ball: 3v (b) red ball: v; cue ball: 2v (c) red ball: 23v; cue ball: v (d) red ball: v; cue ball: 3v (e) The velocities cant be determined without knowing the mass of each ball.

A 5-kg cart moving to the right with a velocity of 16 m/s collides with a concrete wall and rebounds with a velocity of 22 m/s. Is the change in momentum of the cart (a) 0, (b) 40 kg ? m/s, (c) 240 kg ? m/s, (d) 230 kg ? m/s, or (e) 210 kg ? m/s?

A 2-kg object moving to the right with a speed of 4 m/s makes a head-on elastic collision with a 1-kg object that is initially at rest. The velocity of the 1-kg object after the collision is (a) greater than 4 m/s, (b) less than 4 m/s, (c) equal to 4 m/s, (d) zero, or (e) impossible to say based on the information provided.

A 3-kg object moving to the right on a frictionless horizontal surface with a speed of 2 m/s collides head on and sticks to a 2-kg object that is initially moving to the left with a speed of 4 m/s. After the collision, which statement is true? (a) the kinetic energy of the system is 20 J, (b) the momentum of the system is 14 kg ? m/s, (c) the kinetic energy of the system is greater than 5 J but less than 20 J, (d) the momentum of the system is 22 kg ? m/s, (e) the momentum of the system is less than the momentum of the system before the collision.

If two particles have equal kinetic energies, are their momenta equal? (a) yes, always (b) no, never (c) yes, as long as their masses are equal (d) yes, if both their masses and directions of motion are the same (e) no, unless they are moving perpendicular to each other

If two particles have equal momenta, are their kinetic energies equal? (a) yes, always (b) no, never (c) no, except when their masses are equal (d) no, except when their speeds are the same (e) yes, as long as they move along parallel lines

The kinetic energy of a rocket is increased by a factor of eight after its engines are fired, whereas its total mass is reduced by half through the burning of fuel. By what factor is the magnitude of its momentum changed? Hint: Use KE 5 p2/2m. (a) 2 (b) 8 (c) 4 (d) 16 (e) 1

A rocket with total mass 3.00 3 105 kg leaves a launch pad at Cape Kennedy, moving vertically with an acceleration of 36.0 m/s2. If the speed of the exhausted gases is 4.50 3 103 m/s, at what rate is the rocket initially burning fuel? (a) 3.05 3 103 kg/s (b) 2.40 3 103 kg/s (c) 7.50 3 102 kg/s (d) 1.50 3 103 kg/s (e) None of these

Two particles of different mass start from rest. The same net force acts on both of them as they move over equal distances. How do their final kinetic energies compare? (a) The particle of larger mass has more kinetic energy. (b) The particle of smaller mass has more kinetic energy. (c) The particles have equal kinetic energies. (d) Either particle might have more kinetic energy.

An open box slides across a frictionless, icy surface of a frozen lake. What happens to the speed of the box as water from a rain shower falls vertically downward into the box? Explain.

Does a larger net force exerted on an object always produce a larger change in the momentum of the object, compared to a smaller net force? Explain.

Does a larger net force always produce a larger change in kinetic energy than a smaller net force? Explain.

The forces shown in the force vs. time diagram in Figure P6.17 act on a 1.5-kg particle. Find (a) the impulse for the interval from t 5 0 to t 5 3.0 s and (b) the impulse for the interval from t 5 0 to t 5 5.0 s. If the forces act on a 1.5-kg particle that is initially at rest, find the particles speed (c) at t 5 3.0 s and (d) at t 5 5.0 s.

A 3.00-kg steel ball strikes a massive wall at 10.0 m/s at an angle of u 5 60.0 with the plane of the wall. It bounces off the wall with the same speed and angle (Fig. P6.18). If the ball is in contact with the wall for 0.200 s, what is the average force exerted by the wall on the ball?

The front 1.20 m of a 1 400-kg car is designed as a crumple zone that collapses to absorb the shock of a collision. If a car traveling 25.0 m/s stops uniformly in 1.20 m, (a) how long does the collision last, (b) what is the magnitude of the average force on the car, and (c) what is the acceleration of the car? Express the acceleration as a multiple of the acceleration of gravity.

A pitcher throws a 0.14-kg baseball toward the batter so that it crosses home plate horizontally and has a speed of 42 m/s just before it makes contact with the bat. The batter then hits the ball straight back at the pitcher with a speed of 48 m/s. Assume the ball travels along the same line leaving the bat as it followed before contacting the bat. (a) What is the magnitude of the impulse delivered by the bat to the baseball? (b) If the ball is in contact with the bat for 0.005 0 s, what is the magnitude of the average force exerted by the bat on the ball? (c) How does your answer to part (b) compare to the weight of the ball?

High-speed stroboscopic photographs show that the head of a 200-g golf club is traveling at 55 m/s just before it strikes a 46-g golf ball at rest on a tee. After the collision, the club head travels (in the same direction) at 40 m/s. Find the speed of the golf ball just after impact.

A rifle with a weight of 30 N fires a 5.0-g bullet with a speed of 300 m/s. (a) Find the recoil speed of the rifle. (b) If a 700-N man holds the rifle firmly against his shoulder, find the recoil speed of the man and rifle.

A 45.0-kg girl is standing on a 150-kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.50 m/s to the right relative to the plank. (a) What is her velocity relative to the surface of the ice? (b) What is the velocity of the plank relative to the surface of the ice?

This is a symbolic version of Problem 23. A girl of mass mG is standing on a plank of mass mP. Both are originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity vGP to the right relative to the plank. (The subscript GP denotes the girl relative to plank.) (a) What is the velocity vPI of the plank relative to the surface of the ice? (b) What is the girls velocity vGI relative to the ice surface?

An astronaut in her space suit has a total mass of 87.0 kg, including suit and oxygen tank. Her tether line loses its attachment to her spacecraft while shes on a spacewalk. Initially at rest with respect to her spacecraft, she throws her 12.0-kg oxygen tank away from her spacecraft with a speed of 8.00 m/s to propel herself back toward it (Fig. P6.25). (a) Determine the maximum distance she can be from the craft and still return within 2.00 min (the amount of time the air in her helmet remains breathable). (b) Explain in terms of Newtons laws of motion why this strategy works.

A \(75 \mathrm{~kg}\) fisherman in a 125-kg boat throws a package of mass \(m=15 \mathrm{~kg}\) horizontally toward the right with a speed of \(v_{i}=4.5 \mathrm{~m} / \mathrm{s}\) as in Figure P6.26. Neglecting water resistance, and assuming the boat is at rest before the package is thrown, find the velocity of the boat after the package is thrown.

A 65.0-kg person throws a 0.045 0-kg snowball forward with a ground speed of 30.0 m/s. A second person, with a mass of 60.0 kg, catches the snowball. Both people are on skates. The first person is initially moving forward with a speed of 2.50 m/s, and the second person is initially at rest. What are the velocities of the two people after the snowball is exchanged? Disregard friction between the skates and the ice.

An amateur skater of mass M (when fully dressed) is trapped in the middle of an ice rink and is unable to return to the side where there is no ice. Every motion she makes causes her to slip on the ice and remain in the same spot. She decides to try to return to safety by removing her gloves of mass m and throwing them in the direction opposite the safe side. (a) She throws the gloves as hard as she can, and they leave her hand with a velocity vS gloves. Explain whether or not she moves. If she does move, calculate her velocity vS girl relative to the Earth after she throws the gloves. (b) Discuss her motion from the point of view of the forces acting on her.

A man of mass m1 5 70.0 kg is skating at v1 5 8.00 m/s behind his wife of mass m2 5 50.0 kg, who is skating at v2 5 4.00 m/s. Instead of passing her, he inadvertently collides with her. He grabs her around the waist, and they maintain their balance. (a) Sketch the problem with before-and-after diagrams, representing the skaters as blocks. (b) Is the collision best described as elastic, inelastic, or perfectly inelastic? Why? (c) Write the general equation for conservation of momentum in terms of m1, v1, m2, v2, and final velocity vf . (d) Solve the momentum equation for vf . (e) Substitute values, obtaining the numerical value for vf , their speed after the collision.

An archer shoots an arrow toward a 300-g target that is sliding in her direction at a speed of 2.50 m/s on a smooth, slippery surface. The 22.5-g arrow is shot with a speed of 35.0 m/s and passes through the target, which is stopped by the impact. What is the speed of the arrow after passing through the target?

Gayle runs at a speed of 4.00 m/s and dives on a sled, initially at rest on the top of a frictionless, snow- covered hill. After she has descended a vertical distance of 5.00 m, her brother, who is initially at rest, hops on her back, and they continue down the hill together. What is their speed at the bottom of the hill if the total vertical drop is 15.0 m? Gayles mass is 50.0 kg, the sled has a mass of 5.00 kg, and her brother has a mass of 30.0 kg.

A 75.0-kg ice skater moving at 10.0 m/s crashes into a stationary skater of equal mass. After the collision, the two skaters move as a unit at 5.00 m/s. Suppose the average force a skater can experience without breaking a bone is 4 500 N. If the impact time is 0.100 s, does a bone break?

A railroad car of mass 2.00 3 104 kg moving at 3.00 m/s collides and couples with two coupled railroad cars, each of the same mass as the single car and moving in the same direction at 1.20 m/s. (a) What is the speed of the three coupled cars after the collision? (b) How much kinetic energy is lost in the collision?

This is a symbolic version of Problem 33. A railroad car of mass M moving at a speed v1 collides and couples with two coupled railroad cars, each of the same mass M and moving in the same direction at a speed v2. (a) What is the speed vf of the three coupled cars after the collision in terms of v1 and v2? (b) How much kinetic energy is lost in the collision? Answer in terms of M, v1, and v2.

Consider the ballistic pendulum device discussed in Example 6.5 and illustrated in Figure 6.12. (a) Determine the ratio of the momentum immediately after the collision to the momentum immediately before the collision. (b) Show that the ratio of the kinetic energy immediately after the collision to the kinetic energy immediately before the collision is m1/(m1 1 m2).

A car of mass m moving at a speed v1 collides and couples with the back of a truck of mass 2m moving initially in the same direction as the car at a lower speed v2. (a) What is the speed vf of the two vehicles immediately after the collision? (b) What is the change in kinetic energy of the cartruck system in the collision?

In a Broadway performance, an 80.0-kg actor swings from a 3.75-m-long cable that is horizontal when he starts. At the bottom of his arc, he picks up his 55.0-kg costar in an inelastic collision. What maximum height do they reach after their upward swing?

Two shuffleboard disks of equal mass, one orange and the other green, are involved in a perfectly elastic glancing collision. The green disk is initially at rest and is struck by the orange disk moving initially to the right at 5.00 m/s as in Figure P6.38a. After the collision, the orange disk moves in a direction that makes an angle of 37.0 with the horizontal axis while the green disk makes an angle of 53.0 with this axis as in Figure P6.38b. Determine the speed of each disk after the collision.

A 0.030-kg bullet is fired vertically at 200 m/s into a 0.15-kg baseball that is initially at rest. How high does the combined bullet and baseball rise after the collision, assuming the bullet embeds itself in the ball?

An bullet of mass m = 8.00 g is fired into a block of mass M = 250 g that is initially at rest at the edge of a table of height h 5 1.00 m (Fig. P6.40). The bullet remains in the block, and after the impact the block lands d = 2.00 m from the bottom of the table. Determine the initial speed of the bullet. h d m M Figure P6.40

A 12.0-g bullet is fired horizontally into a 100-g wooden block that is initially at rest on a frictionless horizontal surface and connected to a spring having spring constant 150 N/m. The bullet becomes embedded in the block. If the bulletblock system compresses the spring by a maximum of 80.0 cm, what was the speed of the bullet at impact with the block?

A 1 200-kg car traveling initially with a speed of 25.0 m/s in an easterly direction crashes into the rear end of a 9 000-kg truck moving in the same direction at 20.0 m/s (Fig. P6.42 on page 194). The velocity of the car right after the collision is 18.0 m/s to the east. (a) What is the velocity of the truck right after the

A boy of mass mb and his girlfriend of mass mg, both wearing ice skates, face each other at rest while standing on a frictionless ice rink. The boy pushes the girl, sending her away with velocity vg toward the east. Assume that mb . mg. (a) Describe the subsequent motion of the boy. (b) Find expressions for the final kinetic energy of the girl and the final kinetic energy of the boy, and show that the girl has greater kinetic energy than the boy. (c) The boy and girl had zero kinetic energy before the boy pushed the girl, but ended up with kinetic energy after the event. How do you account for the appearance of mechanical energy?

A space probe, initially at rest, undergoes an internal mechanical malfunction and breaks into three pieces. One piece of mass m1 5 48.0 kg travels in the positive x-direction at 12.0 m/s, and a second piece of mass m2 5 62.0 kg travels in the xy-plane at an angle of 105 at 15.0 m/s. The third piece has mass m3 5 112 kg. (a) Sketch a diagram of the situation, labeling the different masses and their velocities. (b) Write the general expression for conservation of momentum in the x- and y-directions in terms of m1, m2, m3, v1, v2, and v3 and the sines and cosines of the angles, taking u to be the unknown angle. (c) Calculate the final x-components of the momenta of m1 and m2. (d) Calculate the final y-components of the momenta of m1 and m2. (e) Substitute the known momentum components into the general equations of momentum for the x- and y-directions, along with the known mass m3. (f) Solve the two momentum equations for v3 cos u and v3 sin u, respectively, and use the identity cos2 u 1 sin2 u 5 1 to obtain v3. (g) Divide the equation for v3 sin u by that for v3 cos u to obtain tan u, then obtain the angle by taking the inverse tangent of both sides. (h) In general, would three such pieces necessarily have to move in the same plane? Why?

A 25.0-g object moving to the right at 20.0 cm/s overtakes and collides elastically with a 10.0-g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision.

A billiard ball rolling across a table at 1.50 m/s makes a head-on elastic collision with an identical ball. Find the speed of each ball after the collision (a) when the second ball is initially at rest, (b) when the second ball is moving toward the first at a speed of 1.00 m/s, and (c) when the second ball is moving away from the first at a speed of 1.00 m/s.

A 90.0-kg fullback running east with a speed of 5.00 m/s is tackled by a 95.0-kg opponent running north with a speed of 3.00 m/s. (a) Why does the tackle constitute a perfectly inelastic collision? (b) Calculate the velocity of the players immediately after the tackle and (c) determine the mechanical energy that is lost as a result of the collision. (d) Where did the lost energy go?

Identical twins, each with mass 55.0 kg, are on ice skates and at rest on a frozen lake, which may be taken as frictionless. Twin A is carrying a backpack of mass 12.0 kg. She throws it horizontally at 3.00 m/s to Twin B. Neglecting any gravity effects, what are the subsequent speeds of Twin A and Twin B?

A 2 000-kg car moving east at 10.0 m/s collides with a 3 000-kg car moving north. The cars stick together and move as a unit after the collision, at an angle of 40.0 north of east and a speed of 5.22 m/s. Find the speed of the 3 000-kg car before the collision.

Two automobiles of equal mass approach an intersection. One vehicle is traveling with velocity 13.0 m/s toward the east, and the other is traveling north with velocity v2i. Neither driver sees the other. The vehicles collide in the intersection and stick together, leaving parallel skid marks at an angle of 55.0 north of east. The speed limit for both roads is 35 mi/h, and the driver of the northward-moving vehicle claims he was within the limit when the collision occurred. Is he telling the truth?

A billiard ball moving at 5.00 m/s strikes a stationary ball of the same mass. After the collision, the first ball moves at 4.33 m/s at an angle of 30 with respect to the original line of motion. (a) Find the velocity (magnitude and direction) of the second ball after collision. (b) Was the collision inelastic or elastic?

In research in cardiology and exercise physiology, it is often important to know the mass of blood pumped by a persons heart in one stroke. This information can be obtained by means of a ballistocardiograph. The instrument works as follows: The subject lies on a horizontal pallet floating on a film of air. Friction on the pallet is negligible. Initially, the momentum of the system is zero. When the heart beats, it expels a mass m of blood into the aorta with speed v, and the body and platform move in the opposite direction with speed V. The speed of the blood can be determined independently (for example, by observing an ultrasound Doppler shift). Assume that the bloods speed is 50.0 cm/s in one typical trial. The mass of the subject plus the pallet is 54.0 kg. The pallet moves at a speed of 6.00 3 1025 m in 0.160 s after one heartbeat. Calculate the mass of blood that leaves the heart. Assume that the mass of blood is negligible compared with the total mass of the person. This simplified example illustrates the principle of ballistocardiography, but in practice a more sophisticated model of heart function is used.

Most of us know intuitively that in a head-on collision between a large dump truck and a subcompact car, you are better off being in the truck than in the car. Why is this? Many people imagine that the collision force exerted on the car is much greater than that exerted on the truck. To substantiate this view, they point out that the car is crushed, whereas the truck is only dented. This idea of unequal forces, of course, is false; Newtons third law tells us that both objects are acted upon by forces of the same magnitude. The truck suffers less damage because it is made of stronger metal. But what about the two drivers? Do they experience the same forces? To answer this question, suppose that each vehicle is initially moving at 8.00 m/s and that they undergo a perfectly inelastic head-on collision. Each driver has mass 80.0 kg. Including the masses of the drivers, the total masses of the vehicles are 800 kg for the car and 4 000 kg for the truck. If the collision time is 0.120 s, what force does the seat belt exert on each driver?

Consider a frictionless track as shown in Figure P6.54. A block of mass m1 5 5.00 kg is released from _. It makes a head-on elastic collision at _ with a block of mass m2 5 10.0 kg that is initially at rest. Calculate the maximum height to which m1 rises after the collision. m1 m2 5.00 m _ _ Figure P6.54

A 2.0-g particle moving at 8.0 m/s makes a perfectly elastic head-on collision with a resting 1.0-g object. (a) Find the speed of each particle after the collision. (b) Find the speed of each particle after the collision if the stationary particle has a mass of 10 g. (c) Find the final kinetic energy of the incident 2.0-g particle in the situations described in parts (a) and (b). In which case does the incident particle lose more kinetic energy?

A bullet of mass m and speed v passes completely through a pendulum bob of mass M as shown in Figure P6.56. The bullet emerges with a speed of v/2. The pendulum bob is suspended by a stiff rod of length , and neglim gible mass. What is the minimum value of v such that the bob will barely swing through a complete vertical circle?

Two objects of masses \(m_1=0.56\mathrm{\ kg}\) and \(m_2=0.88\mathrm{\ kg}\) are placed on a horizontal frictionless surface and a compressed spring of force constant \(\mathrm{k}=280\mathrm{\ N}/\mathrm{m}\) is placed between them as in Figure P6.57a. Neglect the mass of the spring. The spring is not attached to either object and is compressed to a distance of 9.8 cm. If the objects are released from rest, find the final velocity of each object as shown in Figure P6.57b.

A 0.400-kg blue bead slides on a frictionless, curved wire, starting from rest at point _ in Figure P6.58, where h 5 1.50 m. At point _, the bead collides elastically with a 0.600-kg green bead at rest. Find the maximum height the green bead rises as it moves up the wire.

A 730-N man stands in the middle of a frozen pond of radius 5.0 m. He is unable to get to the other side because of a lack of friction between his shoes and the ice. To overcome this difficulty, he throws his 1.2-kg physics textbook horizontally toward the north shore at a speed of 5.0 m/s. How long does it take him to reach the south shore?

An unstable nucleus of mass 1.7 3 10226 kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of m1 5 5.0 3 10227 kg, moves in the positive y- direction with speed v1 5 6.0 3 106 m/s. Another particle, of mass m2 5 8.4 3 10227 kg, moves in the positive x- direction with speed v2 5 4.0 3 106 m/s. Find the magnitude and direction of the velocity of the third particle.

Two blocks of masses m1 and m2 approach each other on a horizontal table with the same constant speed, v0, as measured by a laboratory observer. The blocks undergo a perfectly elastic collision, and it is observed that m1 stops but m2 moves opposite its original motion with some constant speed, v. (a) Determine the ratio of the two masses, m1/m2. (b) What is the ratio of their speeds, v/v0?

Two blocks of masses m1 5 2.00 kg and m2 5 4.00 kg are each released from rest at a height of h 5 5.00 m on a frictionless track, as shown in Figure P6.62 (page 196), and undergo an elastic head-on collision. (a) Determine the velocity of each block just before the collision. (b) Determine the velocity of each block immediately after the collision. (c) Determine the maximum heights to which m1 and m2 rise after the collision. h h m1 m2 Figure P6.62

A block with mass m1 5 0.500 kg is released from rest on a frictionless track at a distance h1 5 2.50 m above the top of a table. It then collides elastically with an object having mass m2 5 1.00 kg that is initially at rest on the table, as shown in Figure P6.63. (a) Determine the velocities of the two objects just after the collision. (b) How high up the track does the 0.500-kg object travel back after the collision? (c) How far away from the bottom of the table does the 1.00-kg object land, given that the height of the table is h2 5 2.00 m? (d) How far away from the bottom of the table does the 0.500-kg object eventually land?

Two objects of masses m and 3m are moving toward each other along the x-axis with the same initial speed v0. The object with mass m is traveling to the left, and the object with mass 3m is traveling to the right. They undergo an elastic glancing collision such that m is moving downward after the collision at right angles from its initial direction. (a) Find the final speeds of the two objects. (b) What is the angle u at which the object with mass 3m is scattered?

A small block of mass m1 5 0.500 kg is released from rest at the top of a curved wedge of mass m2 5 3.00 kg, which sits on a frictionless horizontal surface as in Figure P6.65a. When the block leaves the wedge, its velocity is measured to be 4.00 m/s to the right, as in Figure P6.65b. (a) What is the velocity of the wedge after the block reaches the horizontal surface? (b) What is the height h of the wedge?

A cue ball traveling at 4.00 m/s makes a glancing, elastic collision with a target ball of equal mass that is initially at rest. The cue ball is deflected so that it makes an angle of 30.0 with its original direction of travel. Find (a) the angle between the velocity vectors of the two balls after the collision and (b) the speed of each ball after the collision.

A cannon is rigidly attached to a carriage, which can move along horizontal rails, but is connected to a post by a large spring, initially unstretched and with force constant k 5 2.00 3 104 N/m, as in Figure P6.67. The cannon fires a 200-kg projectile at a velocity of 125 m/s directed 45.0 above the horizontal. (a) If the mass of the cannon and its carriage is 5 000 kg, find the recoil speed of the cannon. (b) Determine the maximum extension of the spring. (c) Find the maximum force the spring exerts on the carriage. (d) Consider the system consisting of the cannon, the carriage, and the shell. Is the momentum of this system conserved during the firing? Why or why not? 45.0 Figure P6.67

The force platform is a tool that is used to analyze the performance of athletes by measuring the vertical force as a function of time that the athlete exerts on the ground in performing various activities. A simplified force vs. time graph for an athlete performing a standing high jump is shown in Figure P6.68. The athlete started the jump at t 5 0.0 s. How high did this athlete jump?

A neutron in a reactor makes an elastic head-on collision with a carbon atom that is initially at rest. (The mass of the carbon nucleus is about 12 times that of the neutron.) (a) What fraction of the neutrons kinetic energy is transferred to the carbon nucleus? (b) If the neutrons initial kinetic energy is 1.6 3 10213 J, find its final kinetic energy and the kinetic energy of the carbon nucleus after the collision.

Two blocks collide on a frictionless surface. After the collision, the blocks stick together. Block A has a mass M and is initially moving to the right at speed v. Block B has a mass 2M and is initially at rest. System C is composed of both blocks. (a) Draw a force diagram for each block at an instant during the collision. (b) Rank the magnitudes of the horizontal forces in your diagram. Explain your reasoning. (c) Calculate the change in momentum of block A, block B, and system C. (d) Is kinetic energy conserved in this collision? Explain your answer. (This problem is courtesy of Edward F. Redish. For more such problems, visit http://www.physics.umd.edu/perg.)

(a) A car traveling due east strikes a car traveling due north at an intersection, and the two move together as a unit. A property owner on the southeast corner of the intersection claims that his fence was torn down in the collision. Should he be awarded damages by the insurance company? Defend your answer. (b) Let the eastward-moving car have a mass of 1 300 kg and a speed of 30.0 km/h and the northward-moving car a mass of 1 100 kg and a speed of 20.0 km/h. Find the velocity after the collision. Are the results consistent with your answer to part (a)?

A 60-kg soccer player jumps vertically upwards and heads the 0.45-kg ball as it is descending vertically with a speed of 25 m/s. (a) If the player was moving upward with a speed of 4.0 m/s just before impact, what will be the speed of the ball immediately after the collision if the ball rebounds vertically upwards and the collision is elastic? (b) If the ball is in contact with the players head for 20 ms, what is the average acceleration of the ball? (Note that the force of gravity may be ignored during the brief collision time.)

A tennis ball of mass 57.0 g is held just above a basketball of mass 590 g. With their centers vertically aligned, both balls are released from rest at the same time, to fall through a distance of 1.20 m, as shown in Figure P6.73. (a) Find the magnitude of the downward velocity with which the basketball reaches the ground. (b) Assume that an elastic collision with the ground instantaneously reverses the velocity of the basketball while the tennis ball is still moving down. Next, the two balls meet in an elastic collision. To what height does the tennis ball rebound?

A 20.0-kg toboggan with 70.0-kg driver is sliding down a frictionless chute directed 30.0 below the horizontal at 8.00 m/s when a 55.0-kg woman drops from a tree limb straight down behind the driver. If she drops through a vertical displacement of 2.00 m, what is the subsequent velocity of the toboggan immediately after impact?

Measuring the speed of a bullet. A bullet of mass m is fired horizontally into a wooden block of mass M lying on a table. The bullet remains in the block after the collision. The coefficient of friction between the block and table is m, and the block slides a distance d before stopping. Find the initial speed v0 of the bullet in terms of M, m, m, g, and d.

A flying squid (family Ommastrephidae) is able to jump off the surface of the sea by taking water into its body cavity and then ejecting the water vertically downward. A 0.85-kg squid is able to eject 0.30 kg of water with a speed of 20 m/s. (a) What will be the speed of the squid immediately after ejecting the water? (b) How high in the air will the squid rise?

A 0.30-kg puck, initially at rest on a frictionless horizontal surface, is struck by a 0.20-kg puck that is initially moving along the x-axis with a velocity of 2.0 m/s. After the collision, the 0.20-kg puck has a speed of 1.0 m/s at an angle of u 5 53 to the positive x-axis. (a) Determine the velocity of the 0.30-kg puck after the collision. (b) Find the fraction of kinetic energy lost in the collision.

A wooden block of mass M rests on a table over a large hole as in Figure P6.78. A bullet of mass m with an initial velocity vi is fired upward into the bottom of the block and remains in the block after the collision. The block and bullet rise to a maximum height of h. (a) Describe how you would find the initial velocity of the bullet using ideas you have learned in this chapter. (b) Find an expression for the initial velocity of the bullet.

A 1.25-kg wooden block rests on a table over a large hole as in Figure P6.78. A 5.00-g bullet with an initial velocity vi is fired upward into the bottom of the block and remains in the block after the collision. The block and bullet rise to a maximum height of 22.0 cm. (a) Describe how you would find the initial velocity of the bullet using ideas you have learned in this chapter. (b) Calculate the initial velocity of the bullet from the information provided.