Question

How long will it take a rock dropped from 2.0 m above the surface of mars to reach the ground?

Answer 1

Answer:

1.038s

Explanation:

To solve this problem we use the following equation for the free fall movement:

$h=v_{i}t+\frac{1}{2} gt^2$

where $h$ is the height, $v_{i}$ is the initial velocity, in this case since the rock was just dropped, $v_{i}=0$, $g$ is the acceleration of gravity of the planet in this case mars, thus g will be: $g=3.711 m/s^2$. And $t$ is time, wich is what we are looking for.

Clearing the equation for $t$ :

$h=v_{i}t+\frac{1}{2} gt^2$

since  $v_{i}=0$

$h=\frac{1}{2} gt^2$

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

$\sqrt{\frac{2h}{g}}=t$

we have $g=3.711 m/s^2$ and from the problem we have that $h=2m$

thus:

$\sqrt{\frac{2(2m)}{3.711m/s^2}}=t$

$\sqrt{\frac{4m}{3.711m/s^2} }=\sqrt{1.0779s^2}=1.038s$

The time it takes is 1.038s