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