Consequences of Relativity Video Lessons

Concept

Problem: A bullet shot from a rifle travels at 1000 m/s. What is the elapsed time between when the bullet strikes a target 500 m away, and when the sound of the gunshot reaches the target? Assume air temperature is 20 °C.

FREE Expert Solution

The time that the bullet takes to strike the target:

$\overline{){{t}}_{{b}}{=}\frac{distance}{speed}}$

The speed of sound in air:

$\overline{){{\mathbf{v}}}_{{\mathbf{s}}}{\mathbf{=}}{\mathbf{\left(}}{\mathbf{331}}{\mathbf{.}}{\mathbf{4}}{\mathbf{+}}{\mathbf{0}}{\mathbf{.}}{\mathbf{6}}{{\mathbf{T}}}_{{\mathbf{c}}}{\mathbf{\right)}}{\mathbf{m}}{\mathbf{/}}{\mathbf{s}}}$, where TC is the temperature of the air.

Time elapsed is:

$\overline{){{\mathbf{t}}}_{\mathbf{e}\mathbf{l}\mathbf{a}\mathbf{p}\mathbf{s}\mathbf{e}\mathbf{d}}{\mathbf{=}}{{\mathbf{t}}}_{{\mathbf{s}}}{\mathbf{-}}{{\mathbf{t}}}_{{\mathbf{b}}}}$, where ts is the time taken by sound.

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Problem Details

A bullet shot from a rifle travels at 1000 m/s. What is the elapsed time between when the bullet strikes a target 500 m away, and when the sound of the gunshot reaches the target? Assume air temperature is 20 °C.