Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 26 - The Special Theory of Relativity - General Problems - Page 770: 75

Answer

a. 15 meters. b. 42 minutes.

Work Step by Step

a. Observers on Earth measure the ship as shorter than the rest length. Use equation 26–3a. $$\mathcal{l}=\mathcal{l}_0\sqrt{1-v^2/c^2}=(23m)\sqrt{1-(0.75)^2}= 15m$$ b. Observers on Earth measure the time interval as longer than the proper time. Use equation 26–1a. $$\Delta t = \frac{\Delta t_0}{\sqrt{1-v^2/c^2}}= \frac{28min}{\sqrt{1-(0.75)^2}}=42min$$
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