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22 January, 20:47

Suppose you fire a rifle bullet at1600 m/s in a shooting gallery and hear the gong on the target ring 0.723 seconds later. taking the speed of sound to be 326 m/s and assuming the bullet travels straight downrange at a constant speed, how many far away is the target?

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  1. 22 January, 21:10
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    The total time would be the sum of time for the bullet to reach the gong and the time it takes the sound to reach you.

    So we have:

    0.723 s = time for bullet to reach gong + time for sound to reach you

    Let us say that D is the distance, then time for bullet to reach gong is D/1600

    While the time for sound to reach you is D/326

    therefore we get

    0.723 = D/1600 + D/326

    D = 0.723 / (1/1600 + 1/326)

    D = 195.8 m
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