Help with physics question
Here is the question:
A cave explorer drops a stone from rest into a hole. The speed of sound is 343m/s in the air, and the sound of the stone striking the bottom is heard 1.50s after the stone is dropped. How deep is the hole?
Thanks in advance!
October 5, 2012
7 Comments • Newest first
[quote=starlight4x]Shouldn't the 1.5s be split onto both sides since it also takes time to reach the ground[/quote]
Only if it falls as quickly as sound spreads
lol nvm
Shouldn't the 1.5s be split onto both sides since it also takes time to reach the ground
Edit: tysm that is the correct answer!
Okay first the stone needs to drop to the bottom, and consider the time it takes for the sound to travel back up for you to hear it.
1. The free fall part: y= vi*t + 1/2 a*(t1)^2, y = 1/2*a*(t1)^2, [b]t1=sqrt[y/4.9][/b]
2. Time it took to return: v=y/t2 = 343, [b]t2 = y/343[/b]
3. Total time it took for you to hear it: [b]1.5 = sqrt[y/4.9] + y/343[/b].
4. Solve for y. y=10.586742 (I graphed this, but you can solve for it by hand if you want to too )
6. It's approx [b]10.6m[/b]
9.8m/sx = 1.5 x 343m
The stone have the reach the ground first to actually create the sound. It's more tricky than it looks
EDIT:
nevermind, misread/plain old retardation