Expert: Sherry Wallin - 11/23/2008

Question
A bullet is fired at a target 4400 feet away. At what point along the path is the impact of the bullet heard 1/4 second before the sound of the gun?

Speed of sound- 1100 feet per second
Speed of bullet- 1650 fps

Thanks for your assistance.

Answer
Hi, try this:
Let s be the distance from where the gun is shot along the line to the
target. Calculate how long it takes for the bullet to get to the target.
Call that time t1.

Calculate how long it took the sound of the bullet to travel to a distance s from the point of fire.

Calculate how long it takes from the time the gun is fired, for the sound of the impact to reach the point at distance s. This is where t1 is needed. Why?

b(s) = time taken for the shot to be heard at distance s.
p(s) = time taken for the impact to be heard at distance s.

Remember both times are from the time of firing.

Ok, now write an equation with h(s), p(s) and 1/4 second that
expresses the problem. Solve that equation for s. Check your
work.

Math Prof