Question

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

Answer 1

1.038s

Step-by-step explanation:

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

`h=v_(i)t+(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+(1)/(2) gt^2`

since
`v_(i)=0`

`h=(1)/(2) gt^2`

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

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

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

thus:

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

`\sqrt{(4m)/(3.711m/s^2) }=√(1.0779s^2)=1.038s`

The time it takes is 1.038s