# free falling question (1 Viewer)

#### somerandomperson

##### New Member
Hikers came across a deep narrow well and decided to find its depth. They dropped a pebble into the well and heard the sound of the pebble hitting the bottom of the well in 7s. Using this information they found the depth of the well. How deep is the well? Assume that the velocity of sound is 340m/s.

I understand there are multiple stages to this question but I've got no idea how to figure them out.

#### Drdusk

##### π
Moderator
Hikers came across a deep narrow well and decided to find its depth. They dropped a pebble into the well and heard the sound of the pebble hitting the bottom of the well in 7s. Using this information they found the depth of the well. How deep is the well? Assume that the velocity of sound is 340m/s.

I understand there are multiple stages to this question but I've got no idea how to figure them out.
You can break it up into two parts.

1 - The time t0 taken for the pebble to drop down to a distance h.
2 - The time taken t1 for the sound to reach the observer from a distance h.

For the first part you can get the equation
$\bg_white h = \dfrac{1}{2}at_0^2$

For the second part you can get the equation
$\bg_white h = 340t_1$

And the final equation which is the 7 seconds it takes for the pebble to fall down and the sound to come up which gives.

$\bg_white 7 = t_0 + t_1$

Now you just have to solve simultaneous equations for t0 and use it to find h which is trivial.