12.0 s
Explanation:
First, let's find the initial vertical velocity of the rock on earth. We know that
vy = v0y - gt
where g = 9.8 m/s^2. When the rock reaches its highest point, vy = 0. So if it takes 2.00 s to reach the maximum height, the initial velocity of the rock is
v0y = (9.8 m/s^2)(2.00 s) = 19.6 m/s.
We know that the moon only has 1/6 of earth's gravity. Therefore, if the same rock is given the same vertical velocity as on earth, then the time it takes to reach its maximum height is
voy = gt ---> t = voy/g
t = (19.6 m/s)/(9.8/6 m/s^2)
= 12.0 s
