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Question: 3 relativistic pingpong in the lectures we determined the paddle...

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(3) Relativistic ping-pon,g In the lectures, we determined the paddle velocity (relative to earth) such that a ball travelling at 10 m/s in the earth frame, would leave the paddle at 15m/s in the earth frame. To solve this problem it was useful to use the paddle-fixed frame. With a heavy (compared to ball) paddle, we could neglect the influence of the ball on the motion of the paddle. Repeat this type of calculation for relativistic speeds using relativistic velocity addition: the ball is travelling at 0.5c relative to the earth. We want the ball to be travelling at 0.75c relative to the earth after the collision (in the opposite direction as compared to before the collision). What should the velocity of the paddle be (relative to the earth)? (You can also assume that the ball velocity is reversed by the collision in the paddle-fixed frame). (Feel free to use rapidities to solve this problem.)

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