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 - Problems - Page 768: 15

Answer

0.9716c.

Work Step by Step

In the Earth’s reference frame, the pion’s average lifetime ($2.6\times10^{-8}s$) of the pion will be dilated, equation 26–1a. Find the speed of the pion as the distance moved in the Earth frame divided by the dilated time. $$v=\frac{d}{\Delta t}=\frac{d}{\Delta t_0}\sqrt{1-v^2/c^2}$$ $$v=c\sqrt{\frac{1}{1+(\frac{c\Delta t_0}{d})^2}}$$ $$v=c\sqrt{\frac{1}{1+(\frac{(3\times10^8 m/s)(2.6\times10^{-8}s)}{32m})^2}}=0.9716c$$
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