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**Arturo_026** **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 $\displaystyle v_0$) 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 : $\displaystyle a(t)=-g$ ; and on Planet X: $\displaystyle a(t)=-g/2$

Then when setting the velocity on Planet X equal to zero, and plugging that $\displaystyle t$ in the position function : $\displaystyle s(t)=(-1/4)gt^2 + v_0t$; supposing that the initial position is zero.

I get: $\displaystyle [(v_0)^2]/g$ 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.