Long Answer. Answer the following questions, showing all work.

1. A 2000 kg train car moving at 3 m/s links with a 3000 kg train car initially at rest. What is the speed of the cars after the collision?

2. Bob, whose mass is 68 kg is rolling on his 2 kg skateboard at 6.0 m/s catches a ball initially traveling at 9.0 m/s in the opposite direction. After Bob catches the ball, he rolls in his original direction at only 4.5 m/s. What is the mass of the ball?

3. A 4.8 kg bowling ball moving at 10 m/s strikes a 1.6 kg bowling pin, initially at rest, head-on. The pin flies forwards at 15 m/s after the collision.

a. What is the final velocity of the bowling ball? b. Is this an elastic or inelastic collision? (Show your work to justify your answer.)

4. A ball (m₁) of mass 0.440kg moving east with a speed of 3.30 m/s collides head-on with a 0.220 kg ball (m₂) at rest. If the collision is perfectly elastic, what will the speed of each ball be after the collision? (Hint: the relationship of the velocities before and after the collision is v_1i- v_2i = v_2f - v_1f. This equation may be useful if you have two unknowns in an equation.)

a. Solve for v_2f in terms of v_1f using the provided information.

b. Using the law of conservation of momentum, substitute your answer from part (a) and solve for the final velocity of the first ball. c. Solve for the final velocity of the second ball.