# 08 - Sound of Impact be Heard Before the Report of the Gun

**Problem**

A bullet is fired at a target 1,342 m away. At what point along its path would the sound of the impact of the bullet be heard 1/4 second before the report of the gun, assuming that sound travels at the rate of 335 m/sec and the bullet is 503 m/sec.

**Answer Key**

182.24 m

**Solution**

$t_{\text{sound of gun}} - (t_{\text{bullet}} + t_{\text{sound of impact}}) = \frac{1}{4}$

$\dfrac{1342 - x}{335} - \left( \dfrac{1342}{503} + \dfrac{x}{335} \right) = \dfrac{1}{4}$

$x = 182.24 ~ \text{m}$ answer

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