Calculating Distance Using Speed and Time: A Kinematics Problem

[Omid]

Hi there,
Please help me with this problem
I read physics on my own so this is not a homework !

Suppose you fire a rifle bullet (1600 m/s) in a shooting gallery and hear the gong on the target ring 0.731 s later.
Taking the speed of sound to be 330 m/s and assuming the bullet travels straight downrange at a constant speed, how far away is the target ?

Here is my work :
Given { (v_1) = 1600 m/s, (v_2) = 330 m/s, t_T = 0.731 }
Find {l}
There is a distance between us and the target ring (l) that the problem asks to find it.
I know that when speed is constant or we know the average speed we can find (l) the distance traveled :
l = t.v
But in the problem we don’t have t_1 ( the time taken by bullet to reach the target ) and we don't have t_2 ( the time taken by sound to reach our ear ) then we must have v_T (The average speed in from firing the bullet till reaching the sound to our ears ) but to finding that we need to know l_T ( the total distance traveled ) so what shall we do ?


Thanks

 

[Doc Al]

Welcome to PF! Don't be afraid to ask questions, as long as you show your work.

Write down what you do know. Start with t_1. Since d = vt, we have:
(1) L = v_{bullet}t_1
And then for t_2, we have:
(2) L = v_{sound}t_2
But we know t_T = t_1 + t_2, so can you find an equation for t_T in terms of the speeds and distance?

 

[Omid]

Yes I can !
With PF I don't feel lonely in the rest of the way in studying physics.
Thank you very much.