Two observers agree to test time dilation. They use identical clocks, and one observer in frame S’ moves with speed v = 0.6c relative to the other observer in frame S. When their origins coincide, they start their clocks. They agree to send each other a signal when their clocks read 60 min and to send a confirmation signal when each receives the other’s signal. (a) When does the observer in S receive the first signal from the observer in S’? (b) When does he(the observer in S)receive the confirmation signal? Answer them using the time in reference frame S.

Physics for Scientists and Engineers: Foundations and Connections
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ISBN:9781133939146
Author:Katz, Debora M.
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Chapter39: Relativity
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Two observers agree to test time dilation. They use identical clocks, and one observer in frame S’ moves with speed v = 0.6c relative to the other observer in frame S. When their origins coincide, they start their clocks. They agree to send each other a signal when their clocks read 60 min and to send a confirmation signal when each receives the other’s signal. (a) When does the observer in S receive the first signal from the observer in S’? (b) When does he(the observer in S)receive the confirmation signal? Answer them using the time in reference frame S.

Expert Solution
Step 1 Lorentz formula

Observer in each frame remains always at x=0 for all values of t. In frameS', x'=0 at all values of t'.

Lorentz transformation formula used are as-

x=rx'+vt'...........1

and t=rt'+vx'c2............2

In this case, r=11-v2c2

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