Question

If an object takes 7 second to fall to the ground, what was its initial height? Show your work.

Answer 1

Answer:240.1 m

Explanation:

We are given the following equation that models the the time it takes to an object to fall to the ground:

`t_((H))=\sqrt{(2H)/(g)}`

Where:

`t_((H))=7 s` is the time it takes to the object to fall to the ground

`H` is the object's initial height

`g=9.8 m/s^(2)` is the acceleration due gravity

Isolating
`H`:

`t^(2)=(\sqrt{(2H)/(g)})^(2)`

`t^(2)=(2H)/(g)}`

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

Solving with the given data:

`H=((7 s)^(2)(9.8 m/s^(2)))/(2)`

`H=240.1 m` This is the initial height