Three identical train cars, coupled together, are rolling

Problem 3CQ Explain the concept of isolated system in nonmathematical language that would make sense to an educated person who had never heard of it.

Problem 75CP You are a world-famous physicist-lawyer defending a client who has been charged with murder. It is alleged that your client, Mr. Smith, shot the victim, Mr. Wesson. The detective who investigated the scene of the crime found a second bullet, from a shot that missed Mr. Wesson, that had embedded itself into a chair. You arise to cross-examine the detective. You: In what type of chair did you find the bullet? Det: A wooden chair. You: How massive was this chair? Det: It had a mass of 20 kg. You: How did the chair respond to being struck with a bullet? Det: It slid across the floor. You: How far? Det: A good three centimeters. The slide marks on the dusty floor are quite distinct. You: What kind of floor was it? Det: A wood floor, very nice oak planks. You: What was the mass of the bullet you retrieved from the chair? Det: Its mass was 10 g. You: And how far had it penetrated into the chair? Det: A distance of 1.5 cm. You: Have you tested the gun you found in Mr. Smith’s possession? Det: I have. You: What is the muzzle velocity of bullets fired from that gun? Det: The muzzle velocity is 450 m/s. You: And the barrel length? Det: The gun has a barrel length of 16 cm. With only a slight hesitation, you turn confidently to the jury and proclaim, “My client’s gun did not fire these shots!” How are you going to convince the jury and the judge?

Problem 2CQ Explain the concept of impulse in nonmathematical language. That is, don’t simply put the equation in words to say that “impulse is the time integral of force.” Explain it in terms that would make sense to an educated person who had never heard of it.

Problem 1E What is the magnitude of the momentum of a. A 3000 kg truck traveling at 15 m/s? ________________ b. A 200 g baseball thrown at 40 m/s?

Problem 2E At what speed do a bicycle and its rider, with a combined mass of 100 kg, have the same momentum as a 1500 kg car traveling at 5.0 m/s?

Rank in order, from largest to smallest, the momenta \(\left(p_{x}\right)_{\mathrm{a}}\) to \(\left(p_{x}\right)_{\mathrm{e}}\) of the objects in FIGURE Q9.1. ________________ Equation Transcription: Text Transcription: (p_x)_a (p_x)_e

What impulse does the force shown in Figure EX9.3 exert on a \(250 g\) particle? ________________ Equation Transcription: Text Transcription: 250 g

Problem 4CQ A 0.2 kg plastic cart and a 20 kg lead cart can roll without friction on a horizontal surface. Equal forces are used to push both carts forward for a time of 1 s, starting from rest. After the force is removed at t = 1 s, is the momentum of the plastic cart greater than, less than, or equal to the momentum of the lead cart? Explain.

What is the impulse on a \(3.0 kg\) particle that experiences the force shown in Figure EX9.4? ________________ Equation Transcription: Text Transcription: 3.0 kg

Problem 6CQ Angie, Brad, and Carlos are discussing a physics problem in which two identical bullets are fired with equal speeds at equal-mass wood and steel blocks resting on a frictionless table. One bullet bounces off the steel block while the second becomes embedded in the wood block. “All the masses and speeds are the same,” says Angie, “so I think the blocks will have equal speeds after the collisions.” “But what about momentum?” asks Brad. “The bullet hitting the wood block transfers all its momentum and energy to the block, so the wood block should end up going faster than the steel block.” “I think the bounce is an important factor,” replies Carlos. “The steel block will be faster because the bullet bounces off it and goes back the other direction.” Which of these three do you agree with, and why?

Problem 7CQ It feels better to catch a hard ball while wearing a padded glove than to catch it bare handed. Use the ideas of this chapter to explain why.

Problem 5CQ A 0.2 kg plastic cart and a 20 kg lead cart can both roll without friction on a horizontal surface. Equal forces are used to push both carts forward for a distance of 1 m, starting from rest. After traveling 1 m, is the momentum of the plastic cart greater than, less than, or equal to the momentum of the lead cart? Explain.

Figure EX9.6 is an incomplete momentum bar chart for a \(50 g\) particle that experiences an impulse lasting \(10 ms\). What were the speed and direction of the particle before the impulse? ________________ Equation Transcription: Text Transcription: 50 g 10 ms

Figure EX 9.7 is an incomplete momentum bar chart for a collision that lasts \(10 ms\). What are the magnitude and direction of the average collision force exerted on the object? ________________ Equation Transcription: Text Transcription: 10 ms

In FIGURE EX9.5, what value of \(F_{\max }\) gives an impulse of \(6.0\ \mathrm{Ns}\)? ________________ Equation Transcription: Text Transcription: F_max 6.0 Ns

A \(2.0 kg\) object is moving to the right with a speed of \(1.0 m/s\) when it experiences the force shown in Figure EX9.8. What are the object’s speed and direction after the force ends? ________________ Equation Transcription: Text Transcription: 2.0 kg 1.0 m/s

Problem 10CQ A 2 kg object is moving to the right with a speed of 1 m/s when it experiences an impulse of —4 Ns. What are the object’s speed and direction after the impulse?

Problem 9CQ A 2 kg object is moving to the right with a speed of 1 m/s when it experiences an impulse of 4 Ns. What are the object’s speed and direction after the impulse?

A 2.0 kg object is moving to the right with a speed of 1.0 m/s when it experiences the force shown in Figure EX9.9. What are the object’s speed and direction after the force ends? ________________ Equation Transcription: Text Transcription: 2.0 kg 1.0 m/s

Problem 10E A sled slides along a horizontal surface on which the coefficient of kinetic friction is 0.25. Its velocity at point A is 8.0 m/s and at point B is 5.0 m/s. Use the impulse-momentum theorem to find how long the sled takes to travel from A to B.

Problem 8CQ Automobiles are designed with “crumple zones” intended to collapse in a collision. Use the ideas of this chapter to explain why.

Problem 11CQ A golf club continues forward after hitting the golf ball. Is momentum conserved in the collision? Explain, making sure you are careful to identify “the system.”

Problem 12CQ Suppose a rubber ball collides head-on with a steel ball of equal mass traveling in the opposite direction with equal speed. Which ball, if either, receives the larger impulse? Explain.

Problem 13CQ Two particles collide, one of which was initially moving and the other initially at rest. a. Is it possible for both particles to be at rest after the collision? Give an example in which this happens, or explain why it can’t happen. ________________ b. Is it possible for one particle to be at rest after the collision? Give an example in which this happens, or explain why it can’t happen.

| A 250 g ball collides with a wall. Figure EX9.12 shows the ball’s velocity and the force exerted on the ball by the wall. What is \(v_{\mathrm{f} x}\), the ball’s rebound velocity? ________________ Equation Transcription: Text Transcription: v_f x

Far in space, where gravity is negligible, a \(425 \mathrm{~kg}\) rocket traveling at \(75 \mathrm{~m} / \mathrm{s}\) fires its engines. Figure EX9.11 shows the thrust force as a function of time. The mass lost by the rocket during these \(30 \mathrm{~s}\) is negligible. a. What impulse does the engine impart to the rocket? b. At what time does the rocket reach its maximum speed? What is the maximum speed? ________________ Equation Transcription: Text Transcription: 4.5 kg 75 m/s 30 s

Problem 14CQ Two ice skaters, Paula and Ricardo, push off from each other. Ricardo weighs more than Paula. a. Which skater, if either, has the greater momentum after the push-off? Explain. ________________ b. Which skater, if either, has the greater speed after the push-off? Explain.

A air-track glider collides with a spring at one end of the track. FIGURE EX9.13 shows the glider's velocity and the force exerted on the glider by the spring. How long is the glider in contact with the spring?

Problem 14E A 10,000 kg railroad car is rolling at 2.00 m/s when a 4000 kg load of gravel is suddenly dropped in. What is the car’s speed just after the gravel is loaded?

Problem 15E A 5000 kg train car, with its top open, is rolling on frictionless rails at 22.0 m/s when it starts pouring rain. A few minutes later, the car’s speed is 20.0 m/s. What mass of water has collected in the car?

Problem 16E A 10-m-long glider with a mass of 680 kg (including the passengers) is gliding horizontally through the ah at 30 m/s when a 60 kg skydiver drops out by releasing his grip on the glider, What is the glider’s velocity just after the skydiver lets go?

Problem 17E A 300 g bird flying along at 6.0 m/s sees a 10 g insect heading straight toward it with a speed of 30 m/s. The bird opens its mouth wide and enjoys a nice lunch. What is the bird’s speed immediately after swallowing?

Problem 18E The parking brake on a 2000 kg Cadillac has failed, and it is rolling slowly, at 1 mph, toward a group of small children. Seeing the situation, you realize you have just enough time to drive your 1000 kg Volkswagen head-on into the Cadillac and save the children. With what speed should you impact the Cadillac to bring it to a halt?

Problem 19E A 1500 kg car is rolling at 2.0 m/s. You would like to stop the car by firing a 10 kg blob of sticky clay at it. How fast should you fire the clay?

Problem 20E A 50 kg archer, standing on frictionless ice, shoots a 100 g arrow at a speed of 100 m/s. What is the recoil speed of the archer?

Problem 21E Dan is gliding on his skateboard at 4.0 m/s. He suddenly jumps backward off the skateboard, kicking the skateboard forward at 8.0 m/s. How fast is Dan going as his feet hit the ground? Dan’s mass is 50 kg and the skateboard’s mass is 5.0 kg.

Problem 22E A 70.0 kg football player is gliding across very smooth ice at 2.00 m/s. He throws a 0.450 kg football straight forward. What is the player’s speed afterward if the ball is thrown at a. 15.0 m/s relative to the ground? ________________ b. 15.0 m/s relative to the player?

Two particles collide and bounce apart. Figure EX9.23 shows the initial momenta of both and the final momentum of particle 2. What is the final momentum of particle 1? Write your answer in component form.

Problem 25E A 20 g ball of clay traveling east at 3.0 m/s collides with a 30 g ball of clay traveling north at 2.0 m/s. What are the speed and the direction of the resulting 50 g blob of clay?

A 60 g tennis ball with an initial speed of 32 m/s hits a wall and rebounds with the same speed. FIGURE P9.26 shows the force of the wall on the ball during the collision. What is the value of \(F_{\max }\), the maximum value of the contact force during the collision? ________________ Equation Transcription: Text Transcription: F_max

An object at rest explodes into three fragments. Figure EX9.24 shows the momentum vectors of two of the fragments. What are \(p_{x}\) and \(p_{y}\) of the third fragment? FIGURE EX9.24 ________________ Equation Transcription: Text Transcription: p_x p_y

Problem 27P A tennis player swings her 1000 g racket with a speed of 10 m/s. She hits a 60 g tennis ball that was approaching her at a speed of 20 m/s. The ball rebounds at 40 m/s. a. How fast is her racket moving immediately after the impact? You can ignore the interaction of the racket with her hand for the brief duration of the collision. b. If the tennis ball and racket are in contact for 10 ms, what is the average force that the racket exerts on the ball?

A \(200 g\) ball is dropped from a height of \(2.0 m\), bounces on a hard floor, and rebounds to a height of \(1.5 m\). Figure P9.28 shows the impulse received from the floor. What maximum force does the floor exert on the ball? ________________ Equation Transcription: Text Transcription: 200 g 2.0 m 1.5 m

A 500 g cart is released from rest 1.00 m from the bottom of a frictionless, \(30.0^{\circ}\) ramp. The cart rolls down the ramp and bounces off a rubber block at the bottom. Figure P9.29 shows the force during the collision. After the cart bounces, how far does it roll back up the ramp? ________________ Equation Transcription: Text Transcription: 30. 0^circ

Problem 30P One week in lab, you’re given a spring-loaded bar that can be used to strike a metal ball. Your assignment is to measure what size impulse the bar delivers to the ball. You and your lab partner decide to place several balls of different mass on the edge of the lab table, use the striker to launch them horizontally, and measure the horizontal distance to where each ball hits the floor. a. Let the table height be h and the horizontal distance traveled by the ball be its range R. Find an expression for the range. The range depends on h, the ball’s mass in, and the impulse J. ________________ b. What should you graph the measured range against to get a linear graph whose slope is related to J? ________________ c. After measuring the table height to be 1.5 m, you and your partner acquire the following data: Mass (g) Range (cm) 100 247 150 175 200 129 250 98

Problem 31P The flowers of the bunchberry plant open with astonishing force and speed, causing the pollen grains to be ejected out of the flower in a mere 0.30 ms at an acceleration of 2.5 × 104 m/s2. If the acceleration is constant, what impulse is delivered to a pollen grain with a mass of 1.0 × 10-7g?

Problem 33P A small rocket to gather weather data is launched straight up. Several seconds into the flight, its velocity is 120 m/s and it is accelerating at 18 m/s2. At this instant, the rocket’s mass is 48 kg and it is losing mass at the rate of 0.50 kg/s as it burns fuel. What is the net force on the rocket? Hint: Newton’s second law was presented in a new form in this chapter.

Problem 34P Three identical train cars, coupled together, are rolling east at 2.0 m/s. A fourth car traveling east at 4.0 m/s catches up with the three and couples to make a four-car train. A moment later, the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five-car train. What is the speed of the five-car train?

Problem 32P A particle of mass m is at rest at t = 0. Its momentum for t > 0 is given by px = 6t2 kg m/s, where t is in s. Find an expression for Fx(t), the force exerted on the particle as a function of time.

Air-track gliders with masses \(300 g, 400 g,\) and \(200 g\) are lined up and held in place with lightweight springs compressed between them. All three are released at once. The \(200 g\) glider flies off to the right while the \(300 g\) glider goes left. Their position-versus-time graphs, as measured by motion detectors, are shown in Figure P9.36. What are the direction (right or left) and speed of the \(400 g\) glider that was in the middle? ________________ Equation Transcription: Text Transcription: 300 g 400 g 200 g 200 g 300 g 400 g

Problem 35P A clay blob of mass m1, initially at rest, is pushed across a frictionless surface with constant force F for a distance d. It then hits and sticks to a second clay blob of mass m2 that is at rest. Find an expression for their speed after the collision.

Most geologists believe that the dinosaurs became extinct 65 million years ago when a large comet or asteroid struck the earth, throwing up so much dust that the sun was blocked out for a period of many months. Suppose an asteroid with a diameter of 2.0 km and a mass of \(1.0 \times 10^{13} \mathrm{~kg}\) hits the earth with an impact speed of \(4.0 \times 10^{4} \mathrm{~m} / \mathrm{s}\). a. What is the earth's recoil speed after such a collision? (Use a reference frame in which the earth was initially at rest.) b. What percentage is this of the earth's speed around the sun? (Use the astronomical data inside the back cover.) ________________ Equation Transcription: Text Transcription: 1.0 X 10^{13} kg 4.0 X 10^{4} m/s

Problem 38P Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse. At the center of a 50-m-diameter circular ice rink, a 75 kg skater traveling north at 2.5 m/s collides with and holds onto a 60 kg skater who had been heading west at 3.5 m/s. a. How long will it take them to glide to the edge of the rink? ________________ b. Where will they reach it? Give your answer as an angle north of west.

Problem 40P Two ice skaters, with masses of 50 kg and 75 kg, are at the center of a 60-m-diameter circular rink. The skaters push off against each other and glide to opposite edges of the rink. If the heavier skater reaches the edge in 20 s, how long does the lighter skater take to reach the edge?

Problem 39P Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse. Squids rely on jet propulsion to move around. A 1.5 kg squid drifting at 0.40 m/s suddenly expels 0.10 kg of water backward to quickly get itself moving forward at 2.5 m/s. If drag is ignored over the small interval of time needed to expel the water (the impulse approximation), with what speed relative to itself does the squid eject the water?

Problem 44P Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse. Fred (mass 60 kg) is running with the football at a speed of 6.0 m/s when he is met head-on by Brutus (mass 120 kg), who is moving at 4.0 m/s. Brutus grabs Fred in a tight grip, and they fall to the ground. Which way do they slide, and how far? The coefficient of kinetic friction between football uniforms and Astroturf is 0.30.

You are part of a search-and-rescue mission that has been called out to look for a lost explorer. You’ve found the missing explorer, but, as Figure P9.45 shows, you’re separated from him by a \(200-m\)-high cliff and a \(30-m\)-wide raging river. To save his life, you need to get a \(5.0 kg\) package of emergency supplies across the river. Unfortunately, you can’t throw the package hard enough to make it across. Fortunately, you happen to have a \(1.0 kg\) rocket intended for launching flares. Improvising quickly, you attach a sharpened stick to the front of the rocket, so that it will impale itself into the package of supplies, then fire the rocket at ground level toward the supplies. What minimum speed must the rocket have just before impact in order to save the explorer’s life? ________________ Equation Transcription: Text Transcription: 200-m 30-m 5.0 kg 1.0 kg

Problem 42P One billiard ball is shot east at 2.00 m/s. A second, identical billiard ball is shot west at 1.00 m/s. The balls have a glancing collision, not a head-on collision, deflecting the second ball by 90° and sending it north at 1.41 m/s. What are the speed and direction of the first ball after the collision?

Problem 41P A firecracker in a coconut blows the coconut into three pieces. Two pieces of equal mass fly off south and west, perpendicular to each other, at 20 m/s. The third piece has twice the mass of the other two. What are the speed and direction of the third piece?

Problem 43P Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse. a. A bullet of mass m is fired into a block of mass M that is at rest. The block, with the bullet embedded, slides distance d across a horizontal surface. The coefficient of kinetic friction is ?k. Find an expression for the bullet’s speed vbullet. ________________ b. What is the speed of a 10 g bullet that, when fired into a 10 kg stationary wood block, causes the block to slide 5.0 cm across a wood table?

In a ballistics test, a 25 g bullet traveling horizontally at 1200 m/s goes through a 30-cm-thick 350 kg stationary target and emerges with a speed of 900 m/s. The target is free to slide on a smooth horizontal surface. What is the target’s speed just after the bullet emerges?

Problem 49P Two 500 g blocks of wood are 2.0 m apart on a frictionless table. A 10 g bullet is fired at 400 m/s toward the blocks. It passes all the way through the first block, then embeds itself in the second block. The speed of the first block immediately afterward is 6.0 m/s. What is the speed of the second block after the bullet stops?

Problem 51P Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse. The stoplight had just changed and a 2000 kg Cadillac had entered the intersection, heading north at 3.0 m/s, when it was struck by a 1000 kg eastbound Volkswagen. The cars stuck together and slid to a halt, leaving skid marks angled 35° north of east. How fast was the Volkswagen going just before the impact?

Problem 46P An object at rest on a flat, horizontal surface explodes into two fragments, one seven times as massive as the other. The heavier fragment slides 8.2 m before stopping. How far does the lighter fragment slide? Assume that both fragments have the same coefficient of kinetic friction.

Problem 50P Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse. II The skiing duo of Brian (80 kg) and Ashley (50 kg) is always a crowd pleaser. In one routine, Brian, wearing wood skis, starts at the top of a 200-m-long, 20° slope. Ashley waits for him halfway down. As he skis past, she leaps into his arms and he carries her the rest of the way down. What is their speed at the bottom of the slope?

Problem 52P Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse. Ann (mass 50 kg) is standing at the left end of a 15-m-long, 500 kg cart that has frictionless wheels and rolls on a frictionless track. Initially both Ann and the cart are at rest. Suddenly, Ann starts running along the cart at a speed of 5.0 m/s relative to the cart. How far will Ann have run relative to the ground when she reaches the right end of the cart?

A 1500 kg weather rocket accelerates upward at \(10 \mathrm{~m} / \mathrm{s}^{2}\). It explodes 2.0 s after liftoff and breaks into two fragments, one twice as massive as the other. Photos reveal that the lighter fragment traveled straight up and reached a maximum height of 530 m. What were the speed and direction of the heavier fragment just after the explosion? ________________ Equation Transcription: Text Transcription: 10 m/s^2

Problem 53P Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse. A ball of mass m and another ball of mass 3m are placed inside a smooth metal tube with a massless spring compressed between them. When the spring is released, the heavier ball flies out of one end of the tube with speed v0. With what speed does the lighter ball emerge from the other end?

Problem 54P Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse. Force Fx =(10 N) sin(27?t/4.0 s) is exerted on a 250 g particle during the interval 0 s ? t ? 2.0 s. If the particle starts from rest, what is its speed at t = 2.0 s?

Problem 55P Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse. A 500 g particle has velocity vx = ? 5.0 m/s at t =? 2 s. Force Fx = (4 ? t2)N is exerted on the particle between t = ? 2 s and t = 2 s. This force increases from 0 N at t = ? 2 s to 4 N at t =0 s and then back to 0 N at t =2s. What is the particle’s velocity at t = 2 s?

Problem 56P . A 30 ton rail car and a 90 ton rail car, initially at rest, are connected together with a giant but massless compressed spring between them. When released, the 30 ton car is pushed away at a speed of 4.0 m/s relative to the 90 ton car. What is the speed of the 30 ton car relative to the ground?

Problem 57P A 75 kg shell is fired with an initial speed of 125 m/s at an angle 55° above horizontal. Air resistance is negligible. At its highest point, the shell explodes into two fragments, one four times more massive than the other. The heavier fragment lands directly below the point of the explosion. If the explosion exerts forces only in the horizontal direction, how far from the launch point does the lighter fragment land?

Problem 58P Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse. A proton (mass 1 u) is shot at a speed of 5.0 × 107 m/s toward a gold target. The nucleus of a gold atom (mass 197 u) repels the proton and deflects it straight back toward the source with 90% of its initial speed. What is the recoil speed of the gold nucleus?

Problem 59P Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse. A proton (mass 1 u) is shot toward an unknown target nucleus at a speed of 2.50 × 106 m/s. The proton rebounds with its speed reduced by 25% while the target nucleus acquires a speed of 3.12 × 105 m/s. What is the mass, in atomic mass units, of the target nucleus?

Figure P9.63 shows a collision between three balls of clay. The three hit simultaneously and stick together. What are the speed and direction of the resulting blob of clay?

Problem 61P Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse. A neutron is an electrically neutral subatomic particle with a mass just slightly greater than that of a proton. A free neutron is radioactive and decays after a few minutes into other subatomic particles. In one experiment, a neutron at rest was observed to decay into a proton (mass 1.67 × 10?27 kg) and an electron (mass 9.11 × 10?31 kg). The proton and electron were shot out back-to-back. The proton speed was measured to be 1.0 × 105 m/s and the electron speed was 3.0 × 107 m/s. No other decay products were detected. a. Was momentum conserved in the decay of this neutron? ________________ b. If a neutrino was emitted in the above neutron decay, in which direction did it travel? Explain your reasoning. ________________ c. How much momentum did this neutrino “carry away” with it?

Problem 60P Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse. The nucleus of the polonium isotope 2l4 Po (mass 214 u) is radioactive and decays by emitting an alpha particle (a helium nucleus with mass 4 u). Laboratory experiments measure the speed of the alpha particle to be 1.92 × 107 m/s. Assuming the polonium nucleus was initially at rest, what is the recoil speed of the nucleus that remains after the decay?

Problem 62P Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse. A 20 g ball of clay traveling east at 2.0 m/s collides with a 30 g ball of clay traveling 30° south of west at 1.0 m/s. What are the speed and direction of the resulting 50 g blob of clay?

Problem 64P Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the impulse. A 2100 kg truck is traveling east through an intersection at 2.0 m/s when it is hit simultaneously from the side and the rear. (Some people have all the luck!) One car is a 1200 kg compact traveling north at 5.0 m/s. The other is a 1500 kg midsize traveling east at 10 m/s. The three vehicles become entangled and slide as one body. What are their speed and direction just after the collision?

In Problems 66 through 69 you are given the equation used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation. b. Finish the solution of the problem, including a pictorial representation. \((0.10 \mathrm{~kg})(40 \mathrm{~m} / \mathrm{s})-(0.10 \mathrm{~kg})(-30 \mathrm{~m} / \mathrm{s})=\frac{1}{2}(1400 \mathrm{~N}) \Delta t\) ________________ Equation Transcription: Text Transcription: (0.10 kg)(40 m/s) - (0.10 kg)(-30 m/s) = frac{1}{2} (1400 N) Delta t

Problem 70CP A 1000 kg cart is rolling to the right at 5.0 m/s. A 70 kg man is standing on the right end of the cart. What is the speed of the cart if the man suddenly starts running to the left with a speed of 10 m/s relative to the cart?

A spaceship of mass \(2.0 \times 10^{6} \mathrm{~kg}\) is cruising at a speed of \(5.0 \times 10^{6} \mathrm{~m} / \mathrm{s}\) when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of \(5.0 \times 10^{5} \mathrm{~kg}\), is blown straight backward with a speed of \(2.0 \times 10^{6} \mathrm{~m} / \mathrm{s}\). A second piece, with mass \(8.0 \times 10^{5} \mathrm{~kg}\), continues forward at \(1.0 \times\) \(10^{6} \mathrm{~m} / \mathrm{s}\). What are the direction and speed of the third piece? ________________ Equation Transcription: Text Transcription: 2.0 X 10^{6} kg 5.0 X 10^{6} m / s 5.0 X 10^{5} kg 2.0 X 10^{6} m / s 8.0 X 10^{5} kg 1.0 X 10^{6} m / s

Problem 69P In Problem you are given the equation used to solve a problem. For this, you are to a. Write a realistic problem for which this is the correct equation. ________________ b. Finish the solution of the problem, including a pictorial representation. (50 g)(vfx)1 + (100 g)(7.5 m/s) = (150 g)(1.0 m/s)

Problem 67P In Problem you are given the equation used to solve a problem. For this, you are to a. Write a realistic problem for which this is the correct equation. ________________ b. Finish the solution of the problem, including a pictorial representation. (600 g)(4.0 m/s) = (400 g)(3.0 m/s) + (200 g)(vix)2

The carbon isotope \({ }^{14} \mathrm{C}\) is used for carbon dating of archeological artifacts. \({ }^{14} \mathrm{C}\) (mass \(2.34 \times 10^{-26} \mathrm{~kg}\) ) decays by the process known as beta decay in which the nucleus emits an electron (the beta particle) and a subatomic particle called a neutrino. In one such decay, the electron and the neutrino are emitted at right angles to each other. The electron (mass \(9.11 \times 10^{-31} \mathrm{~kg}\) ) has a speed of \(5.0 \times 10^{7} \mathrm{~m} / \mathrm{s}\) and the neutrino has a momentum of \(8.0 \times 10^{-24} \mathrm{~kg} \mathrm{~m} / \mathrm{s}\). What is the recoil speed of the nucleus? ________________ Equation Transcription: Text Transcription: ^14 C ^14 C 2.34 X 10^{-26} kg 9.11 X 10^{-31} kg 5.0 X 10^{7} m/s 8.0 X 10^{-24} kg m/s

Problem 68P In Problem you are given the equation used to solve a problem. For this, you are to a. Write a realistic problem for which this is the correct equation. ________________ b. Finish the solution of the problem, including a pictorial representation. (3000 kg)vfx = (2000 kg)(5.0 m/s) + (1000 kg)(? 4.0 m/s)

Problem 72CP A 20 kg wood ball hangs from a 2.0-m-long wire. The maximum tension the wire can withstand without breaking is 400 N. A 1.0 kg projectile traveling horizontally hits and embeds itself in the wood ball. What is the greatest speed this projectile can have without causing the cable to break?

Problem 73CP A two-stage rocket is traveling at 1200 m/s with respect to the earth when the first stage runs out of fuel. Explosive bolts release the first stage and push it backward with a speed of 35 m/s relative to the second stage. The first stage is three times as massive as the second stage. What is the speed of the second stage after the separation?

Problem 74CP You are the ground-control commander of a 2000 kg scientific rocket that is approaching Mars at a speed of 25,000 km/h. It needs to quickly slow to 15,000 km/h to begin a controlled descent to the surface. If the rocket enters the Martian atmosphere too fast it will burn up, and if it enters too slowly, it will use up its maneuvering fuel before reaching the surface and will crash. The rocket has a new braking system: Several 5.0 kg “bullets” on the front of the rocket can be fired straight ahead. Each has a high-explosive charge that fires it at a speed of 139,000 m/s relative to the rocket. You need to send the rocket an instruction to tell it how many bullets to fire. Success will bring you fame and glory, but failure of this $500,000,000 mission will ruin your career. How many bullets will you tell the rocket to fire?