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

The answer is 1.04s.

This is the example of free fall.

Let's start with the kinematic formula:

d = v1*t + 1/2a*t²

where:

d - distance

v1 - initial distance (in free fall v1 = 0)

t - time

a - gravitational acceleration

We have:

d = 2m

a = 3.7 m/s² (on mercury)

t = ?

In free fall, the expression looks like:

d = 0*t + 1/2a*t² = 0 + 1/2a*t²

⇒ d = 1/2a*t²

Now, from here t can be calculated:

t² = d : 1/2a

t² = 2d/a

t = √ (2d/a)

Let's replace the parameters:

t = √ (2 * 2 / 3.7)

t = √ (4/3.7)

t = √1.08

t = 1.04 s