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A ball of mass m moves toward a very heavy wall (effectively infinite mass) with speed v directed along the normal to the wall. The wall moves toward the ball with speed u. Find the speed of the ball after an elastic collision with the wall.

1. u + v away from the wall
2. 2u + v away from the wall
3. |u - v| away from the wall
4. |v - 2u| away from the wall

Correct answer: 2u + v away from the wall

Solution

In the wall's frame the ball approaches at (v + u) and bounces back at (v + u). Transforming back to the ground frame adds the wall's speed u, giving final ball speed = (v + u) + u = v + 2u away from the wall.

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