College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 26 - Problems - Page 1010: 15


(a) $L = 79.2~m$ (b) $\Delta t = 610~ns$ (c) $\Delta t_0 = 528~ns$

Work Step by Step

(a) Let $L_0 = 91.5~m$. We can find the length measured according to the rest frame of the particle: $L = L_0~\sqrt{1-\frac{v^2}{c^2}}$ $L = (91.5~m)~\sqrt{1-\frac{(0.50~c)^2}{c^2}}$ $L = 79.2~m$ (b) We can find the time $\Delta t$ according to Earth observers: $\Delta t = \frac{91.5~m}{(0.50)(3.0\times 10^8~m/s)}$ $\Delta t = 610~ns$ (c) We can find the time $\Delta t_0$ in the rest frame of the particle: $\Delta t_0 = \frac{79.2~m}{(0.50)(3.0\times 10^8~m/s)}$ $\Delta t_0 = 528~ns$
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