# Free fall question -- Dropping a pebble into a well to figure out the depth

rabsta00
Homework Statement:
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.
Relevant Equations:
v=v0-gt
y=y0+v0t-0.5gt^2
t=7s
v=340m/s
v=v0-gt
340=v0-9.8x7
v0=408.6
d=d0+v0t-0.5gt^2
d=0+408.6x7-0.5x0.8x7^2
d=2620.1m

this is what I've done but apparently is incorrect, not sure why or what the proper method is

Homework Helper
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Homework Statement:: 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.
Relevant Equations:: v=v0-gt
y=y0+v0t-0.5gt^2

t=7s
v=340m/s
v=v0-gt
340=v0-9.8x7
v0=408.6
d=d0+v0t-0.5gt^2
d=0+408.6x7-0.5x0.8x7^2
d=2620.1m

this is what I've done but apparently is incorrect, not sure why or what the proper method is
You seem to have completely confused the two stages.
First, the pebble falls to the water. Write an equation for that involving the depth and the time taken.
Second, the sound travels to the top. Write an equation for that involving the depth and the time taken.
Make sure to use different symbols for different variables.

Homework Helper
Gold Member
Welcome rabsta00! Please, consider that everything described in the problem happens in 7 seconds.
The stone travels downwards with steadily increasing velocity, then the waves of sound travel upwards at constant velocity.

Gold Member
There are three unknowns: the depth of the well, the time it takes the pebble to drop and the time it takes for the sound to travel up the well. Since there are three unknowns, it will take three equations to solve the problem. The first equation relates the depth of the well to the time it takes the pebble to drop. The second relates relates the depth of the well to the time it takes for the sound to travel of the well. The third relates the two times.

Homework Helper
Modify ##y=y_0+v_0t+½gt^2## to account for the time it takes for the sound to travel from the bottom of the well to the top. What is the implication of the wording "they dropped a pebble" in respect of this equation? (Take downward as + so that g is positive in the equation)

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