Question

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?

Answer 1

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