College Physics (4th Edition)

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

Chapter 12 - Problems - Page 463: 13

Answer

The train is a distance of $737~m$ away.

Work Step by Step

We can let $v_1 = 5790~m/s$ be the speed of sound in steel and we can use the travel time $t_1$ of the sound waves through steel to write an expression for the distance: $d = v_1~t_1$ Note that $t_2 = t_1+2.1~s$. We can let $v_2 = 331~m/s$ be the speed of sound in air and we can use the travel time $t_2$ of the sound waves throguh the air to write an expression for the distance: $d = v_2~t_2 = v_2~(t_1+2.1~s)$ Since the distance is the same, we can equate the two equations to find $t_1$: $v_1~t_1 = v_2~(t_1+2.1~s)$ $(v_1-v_2)~t_1 = (2.1~s)~v_2$ $t_1 = \frac{(2.1~s)~v_2}{v_1-v_2}$ $t_1 = \frac{(2.1~s)(331~m/s)}{5790~m/s-331~m/s}$ $t_1 = 0.1273~s$ We can find the distance $d$: $d = v_1~t_1 = (5790~m/s)(0.1273~s) = 737~m$ The train is a distance of $737~m$ away.
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