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:
[tex]y-y_{o}=V_{o}.t+\frac{1}{2}g.t^{2}[/tex] (1)
[tex]V=V_{o}-g.t[/tex] (2)
Where:
[tex]y[/tex] is the rock's final position
[tex]y_{o}=0[/tex] is the rock's initial position
[tex]V_{o}=30\frac{m}{s}[/tex] is the rock's initial velocity
[tex]V[/tex] is the final velocity
[tex]t[/tex] is the time the parabolic movement lasts
[tex]g=1.62\frac{m}{s^{2}}[/tex] is the acceleration due to gravity at the surface of the moon
As we know [tex]y_{o}=0[/tex] , equation (2) is rewritten as:
[tex]y=V_{o}.t+\frac{1}{2}g.t^{2}[/tex] (3)
On the other hand, the maximum height is accomplished when [tex]V=0[/tex]:
[tex]V=V_{o}-g.t=0[/tex] (4)
[tex]V_{o}-g.t=0[/tex]
[tex]V_{o}=g.t[/tex] (5)
Finding [tex]t[/tex]:
[tex]t=\frac{V_{o}}{g}[/tex] (6)
Substituting (6) in (3):
[tex]y=V_{o}(\frac{V_{o}}{g})+\frac{1}{2}g(\frac{V_{o}}{g})^{2}[/tex] (7)
[tex]y_{max}=\frac{{V_{o}}^{2}}{2g}[/tex] (8) Now we can calculate the maximum height of the rock
[tex]y_{max}=\frac{{(30m/s)}^{2}}{(2)(1.62m/s^{2})}[/tex] (9)
Finally:
[tex]y_{max}=277.777m[/tex]
