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

Step-by-step explanation:

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

$t_{(H)}=\sqrt{\frac{2H}{g}}$

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 $H$:

$t^{2}=(\sqrt{\frac{2H}{g}})^{2}$

$t^{2}=\frac{2H}{g}}$

$H=\frac{t^{2}g}{2}$

Solving with the given data:

$H=\frac{(7 s)^{2}(9.8 m/s^{2})}{2}$

$H=240.1 m$ This is the initial height