# Homework Help: Using integration to find depth

1. Nov 5, 2012

### jackscholar

1. The problem statement, all variables and given/known data
Your mobile phone drops down a sinkhole. You hear it hit the bottom 8.5 seconds later. How deep is the hole?
Assume there is no air resistance
velocity of sound 334m/s
gravity 9.8m/s
2. Relevant equations

3. The attempt at a solution
I tried integrating the equation using just the acceleration; however, I believe that the velocity of sound needs to be incorporated aswell. So I started with a(t)=9.8 then integrated to get 9.8t +c, then I made t=0 v=0 and so c=0 and integrated again to get 4.9t^2 +c, I'm not sure where to go from here.

Last edited: Nov 5, 2012
2. Nov 5, 2012

### tiny-tim

hi jackscholar!

do it the other way round …

find the time it takes to fall a distance x, then add the time for the sound to return from that distance,

then put that equal to 8.5, and solve for x

3. Nov 5, 2012

### jackscholar

all I can think of is 8.5=9.8x + ?? for some reason I keep going back to 8.5=9.8x+x/334

4. Nov 5, 2012

### tiny-tim

what is the time taken to fall a distance x (from rest)?

5. Nov 5, 2012

### jackscholar

I'm sorry but i have absolutely no idea

6. Nov 5, 2012

### jackscholar

I shall sleep on it. Thank you for all your help, as always you've given me something to think about.

7. Nov 5, 2012

### LawrenceC

Hint:

Determine the time for the sound to go from bottom of pit to top. If depth is y then

dt = y/334 seconds

Use free fall equation to determine depth of hole.

y = 0.5 * a * t^2 where

t = total time minus the time for the sound to get from bottom to top
a = 9.8 m/sec^2