Calculating the Depth of a Well: Stone Drop and Sound Splash Time

[green11]

Homework Statement

A stone is dropped into a well. The sound of the splash is heard 2.30 s later. What is the depth of the well?

Homework Equations

g = -9.8 m/s^2
Vsound in air = 343 m/s

The Attempt at a Solution

I'm not really sure how to start. I know that the time it takes to drop down + the time it takes the sound to go back up must = 2.3 seconds

 

[green11]

<< two threads merged by berkeman >>

 

[jgens]

Well, write out what else you know. What do you know about the distance the stone must fall and the distance the sound waves must travel? What about the time it takes the rock to fall a distance h?

 

[jgens]

For the future, please do not post your homework questions in multiple forums.

 

[diazona]

I know that the time it takes to drop down + the time it takes the sound to go back up must = 2.3 seconds

Try writing an equation for that. I'd suggest using variables like t_\text{drop} t_\text{sound}.

 

[green11]

For the future, please do not post your homework questions in multiple forums.

I'm sorry. I posted it in here first then realized it might better belong in the other one.

 

[green11]

Try writing an equation for that. I'd suggest using variables like t_\text{drop} t_\text{sound}.

t_\text{drop} + t_\text{sound} = 2.3 s

Like that?

 

[green11]

Well, write out what else you know. What do you know about the distance the stone must fall and the distance the sound waves must travel? What about the time it takes the rock to fall a distance h?

The distance the stone falls = The distance the sound waves travel

Also, I know that the equation for free fall distance is:
h = (1/2)(-9.8)t^2

Rearranging this, I got that t = sqrt(-h/4.9)

 

[jgens]

So, from your other thread you said,

t_rock + t_sound = 2.3

You have an expression t_rock. Knowing that the sound waves must travel a distance h with velocity v = 343 m/s can you complete the equation?

 

[green11]

So, from your other thread you said,

t_rock + t_sound = 2.3

You have an expression t_rock. Knowing that the sound waves must travel a distance h with velocity v = 343 m/s can you complete the equation?

Would that just be

sqrt(-h/4.9) + 343h = 2.3 s ??

 

[jgens]

Not quite. Since you're only worried about magnitudes here, we don't need to worry about h being positive or negative, so your equation should read,

2.3 s = sqrt(h/g) + h/v_s

Remember t != v(h), t = h/v or h = vt.

 

[green11]

Thank you!