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Ball P has mass 1 kg and is moving at 21 m/s. Ball Q has mass 2 kg and is moving at 4 m/s directly toward P. They undergo a head-on collision. After the collision, P continues in its original direction at 1 m/s. Which of the following statements is/are correct? (I) The speed of Q after the collision is 6 m/s, directed opposite to its initial direction of motion. (II) The coefficient of restitution e = 0.2. (III) The kinetic energy lost in the collision is 200 J. (IV) The magnitude of the impulse exchanged between the two balls is 400 N-s.

1. I, II and III only
2. I and II only
3. II and III only
4. IV only

Correct answer: I, II and III only

Solution

Momentum conservation yields v_Q = +6 m/s (opposite Q's initial motion), giving e = 5/25 = 0.2 and KE loss = 236.5 - 36.5 = 200 J — statements I, II, III are all correct. The impulse on Q is 2*(6-(-4)) = 20 N-s, not 400 N-s, so statement IV is false.

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