Conceptual Physics (12th Edition)

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

Chapter 35 - Think and Solve: 45

Answer

According to the observer on the Earth, the taxi’s clock is running slowly, and the trip took 1.15 hours, earning the driver (1.15 hours)(10 stellars/hour) = 11.5 stellars.

Work Step by Step

Find $\gamma$ at v = 0.50c. It is $\frac{1}{\sqrt{1-v^{2}/c^{2}}}$, or $\frac{1}{\sqrt{1-0.50^{2}}}$, which is 1.15. The factor $\gamma$ is the time dilation factor. Multiplying 1 hour by $\gamma$ gives 1.15 hours.
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