# Calculate the Depth of a Well: u, a and Time Given

• milto
In summary, the conversation discusses finding the depth of a well using equations involving initial speed, drop time, acceleration, echo time, and total time. The equations presented are Depth = InitialSpeed*DropTime + 0.5*Acceleration*DropTime² and SpeedOfSound = Depth/EchoTime. The result of 35.28m is given as a possible solution, but its accuracy is uncertain.
milto

## Homework Statement

How deep is the well remember its takes him 3.8 seconds to hear the stone hit the bottom not 3.8 to see it hit the bottom.
u=0ms^-1
a=10ms^-2

## Homework Equations

Not 100% sure what equations to use becuase my teacher goes to quickly

## The Attempt at a Solution

Would you be able to show me the equations to use to solve it.
Thanks Nick.

Try these

Depth = InitialSpeed*DropTime + 0.5*Acceleration*DropTime²

SpeedOfSound = Depth/EchoTime

TotalTime = DropTime + EchoTime

Thanks mate, I got 35.28m for the depth of the well, is that correct??

Dunno mate! I didn't get that far.

## 1. How do I calculate the depth of a well using 'u', 'a', and time?

To calculate the depth of a well, you will need to use the equation: d = ut + (1/2)at^2. 'd' represents the depth of the well, 'u' is the initial velocity, 'a' is the acceleration due to gravity, and 't' is the time it takes for the object to reach the bottom of the well. Plug in the given values for 'u', 'a', and time and solve for 'd'.

## 2. What is the unit of measurement for the depth of a well?

The unit of measurement for the depth of a well is typically in meters (m) or feet (ft).

## 3. Can I use this equation for any type of well?

This equation is specifically for calculating the depth of a well that is open at the top and has a constant acceleration due to gravity. It may not be applicable for other types of wells, such as closed or non-uniform wells.

## 4. What if I don't know the initial velocity or acceleration?

If you do not have the initial velocity or acceleration, you can use other equations and information to solve for these values. For example, if you know the total distance traveled and the time, you can use the equation d = rt to find the initial velocity. Or, if you know the mass and force acting on the object, you can use Newton's second law (F=ma) to find the acceleration.

## 5. How accurate is this equation for calculating the depth of a well?

The accuracy of this equation will depend on the accuracy of the given values and the assumptions made about the well. For example, this equation assumes a constant acceleration due to gravity and does not account for friction or other external forces. It is important to use precise and accurate measurements for 'u', 'a', and time to get the most accurate calculation of the well's depth.

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