# Distance of the target after hearing the impact of the shot.

A bullet is fired horizontally at a target, and the should of its impact is heard 1.5 seconds later. If the speed of the bullet is 3300 m/sec and the speed of should is 1100 m/sec how far away is the target.

If the speed of the bullet is 3 times faster than the speed of sound, that means a third of the 1.5 seconds should be the time it take for the bullet to travel to the target and the remaining time should be the time it take for the sound to travel back to the shooter. So the time of the bullet to the target should be 0.5 seconds 1 second is the speed of sound back to the ear.

I should be able to use speed x time to determine the distance of target. 1100 x 0.5 seconds = 550 meters. Yet thats not the answer. What is wrong about my assumptions of this problem ?

Your observation that the speed is three times is an important one, but the thing to remember is that it means that time of bullet to target is $\frac{1}{4}$ of 1.5 seconds. That is because since speed is three times, it means that time is one-third. That means that the ratio of times is $1:3$. So this means the bullet's time is 1/4, and not 1/3. So bullet travels for 3/8 seconds. Distance is $\frac{3}{8} \times 3300$.