Question

A stone is dropped from a tower 100 meters above the ground. The stone falls past ground level and into a well. It hits the water at the bottom of the well 5.00 seconds after being dropped from the tower. Calculate the depth of the well. Given: g = -9.81 meters/second2.

Answer 1

First you need to calculate the velocity of the stone when it reaches the ground level. This is easy to find from energy conservation, since the potential energy it had at the top of the tower has been totally converted into kinetic energy.

`mgh= (1)/(2)m v^(2)`
We don't know the mass of the stone, but it cancels from both equations. This gives
`v= √(2gh)` so v=44.27 m/s.

Now, the time it took the stone to fall from the top of the tower to the ground is calculated easily from
`h_(f)= h_(0)+ v_(0)t+ (1)/(2)g t^(2)` .
The initial velocity is 0, the initial height is 100 meters and the final height is 0 since we are taking the ground floor as height 0.
This gives
`t= \sqrt{ ( 2h_(0) )/(g) } = \sqrt{ (200)/(9.8) } = 4.52 s.`
So the time it took the stone to fall from the ground level to the bottom of the well is 5-4.52=0.48 s.

We can now use
`x_(f)=vt+ (1)/(2)g t^(2)` where v is the velocity we calculated before v=44.27 m/s, time is t=0.48 s and xf is the depth of the well.

`x_(f) =44.27*0.48+ (1)/(2)*9.8* 0.48^(2) =22.37 m`
So the solution is 22.5 m

Answer 2

22.5 meters

Step-by-step explanation:

IN order to solve this you just have to use the formula for free fall:

`H=(1)/(2)*g*t^(2)`

Now we insert the values into the formula, we know time, 5 seconds:

`H=(1)/(2)*g*t^(2)\\H=(1)/(2)*-9.8*5^(2)\\h=-122.5`

So we know that the total height fmor the tower to the bottom of the well is 122.5, so we just withdraw the 100 meters that the tower is above the ground and we have that the depth of the well is 22.5 meters.