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

• rabsta00
In summary: When you include the speed of sound, the equation becomes:y=y0+v0t-0.5gt^2 In summary, when a hiker drops a stone into a well, the stone falls at a steady speed and the waves of sound travel up the well at a constant speed.
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

rabsta00 said:
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.

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.

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.

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)

Last edited:
neilparker62 said:
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)
There's a lot more wrong than that. Note the equation that includes the speed of sound and g.(!)

## 1. What is free fall?

Free fall is a term used in physics to describe the motion of an object falling under the influence of gravity alone, with no other forces acting on it.

## 2. How is free fall related to dropping a pebble into a well?

Dropping a pebble into a well is an example of free fall because the pebble is only under the influence of gravity as it falls towards the bottom of the well.

## 3. How can dropping a pebble into a well help figure out its depth?

By measuring the time it takes for the pebble to hit the bottom of the well, and using the equation d = 1/2gt^2 (where d is the depth, g is the acceleration due to gravity, and t is the time), the depth of the well can be calculated.

## 4. Are there any factors that could affect the accuracy of this method?

Yes, factors such as air resistance, the size and shape of the pebble, and the initial velocity of the pebble could all affect the accuracy of the calculation.

## 5. Is this method of determining depth limited to wells?

No, this method can also be used to determine the depth of other vertical holes or crevices, such as a mine shaft or a canyon.

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