Motion question

Question

A bullet is shot from a pistol and travels at a speed of 200 m/s, hitting its target 1.5 km away. How long will it take, from when the gun is fired, for the shooter to hear the sound of the bullet hitting the target? 

Answer 1

You need to know the speed of sound at the temperature of the air between the pistol and the target.  That was not provided in the problem statement.  Call it "a".

 

t₁ = time for bullet to reach the target = d/v = (1500 m)/(200 m/s) = 7.5 s

 

t₂ = time it takes for the sound of the bullet impacting the target to reach the position of the shooter

 

t₂ = d/a = (1500 m) / a

 

t = t₁ + t₂ = time from when pistol is shot until sound of impact on target reaches shooter

 

t = (7.5 s) + (1500 m) / a, where a = speed of sound at the temperature of the air, in m/s.