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.