An ideal superball clock features a ball bouncing back and forth between two walls in gravity-free space. The walls are a distance D apart, and the ball moves with constant speed vo, so the round-trip time is T = 2D/vo. An identical clock in a spaceship moves past us to the right at speed V. The walls are separated by a distance D in the ship frame, and the ball moves with speed to relative to the ship. From our point of view the ball moves diagonally, as shown below.

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As measured in our frame, the horizontal component of the ball's velocity is 2v, while the vertical compenent of the ball's velcolity is √(v02 - v2). How long will it take the ship-clock to tick once (a.k.a, for the ball to bounce once back and forth)?

D
Transcribed Image Text:D
An ideal superball clock features a ball bouncing back and forth between two
walls in gravity-free space. The walls are a distance D apart, and the ball moves
with constant speed vo, so the round-trip time is T = 2D/vo. An identical clock
in a spaceship moves past us to the right at speed V. The walls are separated by
a distance D in the ship frame, and the ball moves with speed vo relative to the
ship. From our point of view the ball moves diagonally, as shown below.
Transcribed Image Text:An ideal superball clock features a ball bouncing back and forth between two walls in gravity-free space. The walls are a distance D apart, and the ball moves with constant speed vo, so the round-trip time is T = 2D/vo. An identical clock in a spaceship moves past us to the right at speed V. The walls are separated by a distance D in the ship frame, and the ball moves with speed vo relative to the ship. From our point of view the ball moves diagonally, as shown below.
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