Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 36 - Relativity - Exercises and Problems - Page 1098: 12

Answer

The light from bolt 1 reaches the assistant $4.0\times 10^{-5}~s$ earlier.

Work Step by Step

We can find the time it takes the light from bolt 1 to reach you: $t_1 = \frac{d}{c} = \frac{9000~m}{3.0\times 10^8~m/s} = 3.0\times 10^{-5}~s$ We can find the time it takes the light from bolt 2 to reach you: $t_2 = \frac{d}{c} = \frac{3000~m}{3.0\times 10^8~m/s} = 1.0\times 10^{-5}~s$ Since the light arrives at the same time, the flash from bolt 1 must have left $2.0\times 10^{-5}~s$ earlier. We can find the time it takes the light from bolt 1 to reach the assistant: $t_1 = \frac{d}{c} = \frac{3000~m}{3.0\times 10^8~m/s} = 1.0\times 10^{-5}~s$ We can find the time it takes the light from bolt 2 to reach the assistant: $t_2 = \frac{d}{c} = \frac{9000~m}{3.0\times 10^8~m/s} = 3.0\times 10^{-5}~s$ Since the light from bolt 1 left $2.0\times 10^{-5}~s$ earlier, and it takes $2.0\times 10^{-5}~s$ less time to travel to the assistant, the light from bolt 1 reaches the assistant $4.0\times 10^{-5}~s$ earlier.
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