The Relativistic Ping-Pong Ball · AI Generator #GEN-B36D9377

Physics

Problem

A futuristic ping-pong table is constructed on a spaceship moving at high speed. The table has length

L = 2.74\;\text{m}

in the ship's rest frame. Player A sits at one end and hits a ball toward Player B at the other end. In the ship's frame, the ball travels at constant speed

v = 0.60c

and takes time

\Delta t = 15.2\;\text{ns}

to cross the table. An observer on Earth watches this game through a window as the spaceship flies by. The Earth observer measures the time for the ball to cross the table as

\Delta t' = 25.0\;\text{ns}

. (a) What is the speed of the spaceship relative to Earth? (b) What is the speed of the ping-pong ball as measured by the Earth observer? (c) What is the length of the ping-pong table as measured by the Earth observer?

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