Is the ball's height the same on Earth and Mars?

[sub7]

Hi,
I understand that if a ball is dropped on Earth and dropped on mars, the ball will reach the same height on both planets thanks the law of conservation of energy. Can anyone prove this mathematically?
Thanks in advance

 

[Simon Bridge]

Welcome to PF;
Sure - just work your way through the ballistics.
The ball reaches the same height it started from - in the absence of air resistance.

But if your idea is to prove the law of conservation of energy...
https://www.physicsforums.com/threads/proof-of-the-law-of-conservation-of-energy.359037/

 

[russ_watters]

Welcome to PF!

Conservation of energy is about as simple as physical laws get: x=x. How you prove it I guess depends on how detailed you want to be, but no matter what you do, everything in it cancels-out to x=x.