A ball moves to the right with speed 10 m/s and collides with a massive vertical wall moving to the right at 2 m/s. The coefficient of restitution is e = 1/2. The wall speed is unchanged. If the ball moves after collision with velocity −N m/s, find N.
Physics · Center of maas , Momentum and Collision · collision and types of collision
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Question

A ball moves to the right with speed 10 m/s and collides with a massive vertical wall moving to the right at 2 m/s. The coefficient of restitution is e = 1/2. The wall speed is unchanged. If the ball moves after collision with velocity −N m/s, find N.

Physics · Center of maas , Momentum and Collision · collision and types of collision

G1 Physics · Accepted Answer

Use relative velocity because the wall is moving. Before collision, relative approach speed of the ball with respect to the wall is u(rel) = 10 − 2 = 8 m/s. After collision, let ball velocity be v. For separation, the wall moves away from the ball with relative speed v(rel) = 2 − v. Coefficient of restitution: e = (relative speed of separation)/(relative speed of approach) 1/2 = (2 − v)/8. Therefore 2 − v = 4 ⇒ v = −2 m/s. Given v = −N m/s, N = 2.