Conceptual Physics (12th Edition)

Published by Addison-Wesley
ISBN 10: 0321909100
ISBN 13: 978-0-32190-910-7

Chapter 35 - Think and Solve: 40

Answer

See below.

Work Step by Step

According to the observer on the planet, the nap appears to last 35 minutes. Find $\gamma$ at v = 0.99c. It is $\frac{1}{\sqrt{1-v^{2}/c^{2}}}$, or $\frac{1}{\sqrt{1-0.99^{2}}}$, which is 7.09. The factor $\gamma$ is the time dilation factor. Multiplying 5 minutes by $\gamma$ gives 35.4 min. According to the observer on the planet, the passenger’s watch is running slowly, and the nap lasted 35.4 minutes.
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