Finding height of a well using speed of sound

[barge56]

Homework Statement

The problem is you drop a coin into a well then 3 second later you hear the splash. With this information find out the height of the well.

Assume 343 m/s is the speed of sound and neglect any effects due to air resistance.

g = acceleration due to gravity = 9.8 m/s^2
v0 = initial velocity = 0 m/s
v1 = final velocity
H = height
t1 = initial time = 0 s
t2 = time at final velocity

Homework Equations

H = (v0^2 - v1^2)/2g

v1 = v0 - g(t2 - t1)

The Attempt at a Solution

Reduced equation to H = v0^2/2g and found v0 to be -9.8m/s^2(3s - 343m/s(t2))

I'm mainly having trouble trying to find out how much time was taken off for the sound of the splash reaching you.

Any help is appreciated.

 

[Doc Al]

The Attempt at a Solution

Reduced equation to H = v0^2/2g and found v0 to be -9.8m/s^2(3s - 343m/s(t2))

Instead of trying to relate distance to speed, which you have no information about, relate distance to time. Use a different kinematic relationship.

I'm mainly having trouble trying to find out how much time was taken off for the sound of the splash reaching you.

Think of the total time as having two parts:
(1) The time it takes for the coin to reach the water
(2) The time it takes for the sound to go from the water to the top of the well

For the second time, realize that sound travels at a constant speed.

 

[Jebus_Chris]

The coin falls down to the bottom of the well in time $$t_1$$. The sound travels up, at velocity s, to your ear in time $$t_2$$. Now we can write 3 basic equations.

<< equations deleted by berkeman >>

We have three unknowns and threee equations, that means that we can solve and figure out h.

 

[berkeman]

The coin falls down to the bottom of the well in time $$t_1$$. The sound travels up, at velocity s, to your ear in time $$t_2$$. Now we can write 3 basic equations.

<< equations deleted by berkeman >>

We have three unknowns and threee equations, that means that we can solve and figure out h.

Please let the OP figure out those equations on their own. They must do the bulk of the work on their homework/coursework problems.