Calculate the Depth of a Well by Solving Free Fall Problems in 4 seconds

[tintin]

Homework Statement

You drop a stone into a deep well and hear it hit the bottom 4.00 s later. This is the time it takes for the stone to fall to the bottom of the well, plus the time it takes for the sound of the stone hitting the bottom to reach you. Sound travels about 343 m/s in air. How deep is the well?

Homework Equations

distance traveled by stone = distance traveled by sound

v0 t + 1/2 at square = v0t + 1/2 at square

The Attempt at a Solution

0 +1/2 * 9.8 * t square = 343 ( 4-t) +0

 

[kuruman]

0 +1/2 * 9.8 * t square = 343 ( 4-t) +0

So far so good. Can you solve this equation for t?

 

[dacruick]

I am not sure you are on the right track with what you are doing. First, you know that the well is x meters deep. and that it takes x/343 seconds for the sound to travel to the top. so that means that the stone takes (4-x/343) seconds to fall. You know that initial velocity is 0 so you are left with the following equation.

x = ((-9.8) * (4 - x/343)²)/2

it will be a quadratic that you have to solve.

Cheers