How Deep is the Hole? Solving for Distance Using Kinematics and Speed of Sound

[Chiralic]

Homework Statement

a stone is dropped from rest into a hole. the speed of sound is 343 m/s in air. the sound of the stone striking bottom is heard 1.5s after the stone is dropped, how deep is the hole?

Homework Equations

kinematics equations

The Attempt at a Solution

not a clue. I know that in 1.5 s it has to drop, hit bottom, and the sound of it travels at 343 m/s back up to vi.

 

[Doc Al]

You're on the right track, just express it mathematically.
Total time = time for stone to fall X meters + time for sound to travel X meters.

(Then you can solve for X.)

 

[Chiralic]

Ok, I understand what your saying, but how do I do this with so many missing variables? if 1.5s = dt + dt...but I don't have either d or t for the stone or sound. or can I somehow use: total T = 1/2 at2(squared) + something with speed of sound...Its just on the tip of my brain! or is my logic way off...

 

[Doc Al]

Hint: The stone and the sound waves both travel the same distance. For the stone: Use falling body kinematics to express the distance as a function of time (t_1). For the sound waves: Express the distance they travel in terms of the speed of sound and time (t_2).

Now you can put it all together by using these facts:
(1) The distance traveled is the same
(2) t_1 + t_2 is given

Then you can solve for the times and then the distance. Just jump in and try it.