**Suppose the acceleration of gravity of planet X is one-half that on the earth. Determine the initial velocity of the ball on the earth (in terms of ) so that the maximum height attained is the same as on planet X.**
What I tought was, first to find what the maximum height in planet X is.

So, having g as my constant for gravity I have:

On Earth :

; and on Planet X:

Then when setting the velocity on Planet X equal to zero, and plugging that

in the position function :

; supposing that the initial position is zero.

I get:

as the maximum height on planet X.

Once I get that answer I try to set it equal to the position function of Earth, but it doesn't seem to work out well. And I'm not even sure if that's what I should do.

Any help would be greatly appreciated.