Question

Relativistic ping-pong In the lectures, we determined the paddle velocity (relative to earth) such that a ball travelling at 10m/s in the earth frame, would leave the paddle at 15 m/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 bal 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.)

Answer 1

VAB =VA-VB

VAB=velocity of A with respect to B

VBP=VB-VP

VBP=velocity of BALL with respect to PADDLE

VB=velocity of BALL with respect to EARTH

VP=velocity of PADDLE with respect to B

From initial data

15=VB-VP

15=10-VP

VP=-5m/s

Now in 2nd case

VP=0.75c-0.25c

=0.5c