# Homework Help: Calculating the depth of a well, when you hear a coin 1.5 secs after youve tworn it

1. Oct 6, 2008

### pivu0

1. The problem statement, all variables and given/known data
You throw a coin into a well, 1.5 seconds later you hear a splash

the acceleratoin is g, 9.81 m/s², the beginnig speed is 0

2. Relevant equations

x= x0 + v0t + (at²)/2

3. The attempt at a solution

x= 0+0+ (9.81*1.5²)/2

x= 11.04 m

Yet this is not the sulotion.
I think I have to use the speed of sound into the eqation (340m/s right?), however I have no idea where I have to do this...

2. Oct 6, 2008

### jamesrc

Re: Calculating the depth of a well, when you hear a coin 1.5 secs after youve tworn

The coin didn't fall for 1.5 seconds, it fell for some time t1 and then it took some time t2 for the sound to travel back to you. t1+t2 = 1.5seconds. The distance it fell is equal to the distance sound will travel in t2 seconds (speed of sound *t2). When you set it up, you'll have 2 equations and 2 unknowns; after solving for t2, multiply that by the speed of sound to get the answer...

3. Oct 6, 2008

### pivu0

Re: Calculating the depth of a well, when you hear a coin 1.5 secs after youve tworn

x= 0+0+(9.81*t1²)/2

x=t2*speed of sound

x=x

(9.81*t1²)/2=t2*speed of sound

so (9.81*t1²)/ (2*speed of sound)= t2

1.5s= t1+t2
1.5s= t1 + ((9.81*t1²)/ (2*speed of sound)

Like this?

4. Oct 6, 2008

### pivu0

Re: Calculating the depth of a well, when you hear a coin 1.5 secs after youve tworn

Anyone? Is this correct?

5. Oct 6, 2008

### mgb_phys

Re: Calculating the depth of a well, when you hear a coin 1.5 secs after youve tworn

Looks ok, do you get reasonable answers?

6. Oct 6, 2008

### pivu0

Re: Calculating the depth of a well, when you hear a coin 1.5 secs after youve tworn

Yes I do :)

It takes the coin 1.469 s to reach the bodom and the sound does 0.031s for reaching the top again!

The well is 10.59m deep :)

7. Oct 6, 2008

### mgb_phys

Re: Calculating the depth of a well, when you hear a coin 1.5 secs after youve tworn

Well done - ;)
It's amazing how many people will get an answer almost correct - make a little mistake but then happily write down any riduculous answer that their calculator tells them without any further thinking!

Last edited: Oct 6, 2008
8. Oct 6, 2008

### D H

Staff Emeritus
Re: Calculating the depth of a well, when you hear a coin 1.5 secs after youve tworn

Are you talking about the answer in the OP, or the answer in post #6? The answer in post #6 looks correct to me.

9. Oct 6, 2008

### mgb_phys

Re: Calculating the depth of a well, when you hear a coin 1.5 secs after youve tworn

Yes, I was congratulating the OP on actualy checking that the answer was reasonable rather than just writing it down, following from my previous question.
Somebody in another question wrote an answer like t=1234567890.12345678901234567890 and said it must have been correct because they used Matlab to get all the decimal places!!!

Sorry reading the reply now it isn't clear ! I should have said that it was correct.

10. Oct 6, 2008

### pivu0

Re: Calculating the depth of a well, when you hear a coin 1.5 secs after youve tworn

Thank you all!

It's not that hard if you think about it.

It's just that I'm used to using a eqation directly after hearing a problem, I should first think it easy, Like the 1.5s= t1+t2 and that they both have the same x....