Arock is projected upward from the surface of the moon, at time t = 0.0 s, w a velocity of 30 m/s. the acceleration due to gravity at the surface of the moon in 1.62 m/s2. what is the maximum height of the rock above the surface?

Explanation:

The situation described here is parabolic movement. However, as we are told that the rock was projected upward from the surface, we will only use the equations related to the Y axis.

In this sense, the movement equations in the Y axis are:

   (1)

   (2)

Where:

 is the rock's final position

 is the rock's initial position

is the rock's initial velocity

is the final velocity

is the time the parabolic movement lasts

 is the acceleration due to gravity at the surface of the moon

As we know , equation (2) is rewritten as:

   (3)

On the other hand, the maximum height  is accomplished when :

   (4)

   (5)

Finding :

   (6)

Substituting (6) in (3):

   (7)

   (8)  Now we can calculate the maximum height of the rock

  (9)

Finally: