# 01 - Sound of impact of the bullet hitting the target

**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.

**Solution**

t

$t_1 = \dfrac{1342 - x}{335}$

_{1}= time for the sound of gun to reach the observer$t_1 = \dfrac{1342 - x}{335}$

$t_1 = \dfrac{1342}{335} - \dfrac{x}{335}$

t_{2} = time for the sound of impact to reach the observer

$t_2 = \dfrac{1342}{503} + \dfrac{x}{335}$

$t_1 - \frac{1}{4} = t_2$

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

$\dfrac{2}{335}x = 1.088$

$x = 182.24 ~ \text{m from the target}$ *answer*

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