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Originally Posted by monsieurcoffee
Er... I am currently taking AP Physics so I am not very experienced with it. But it seems to me that you are saying: Potential Energy = Kinetic Energy... Well, when the robot is hanging it's got PE, but no KE... I think it was lucky that when solving for 'h', you came out with v^2/2g
I used Andy's method of applying the equation "V^2=Vo^2+2aX" and derived the same formula.. Hmmmmm.
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Mike's equation comes from the fact that energy must be conserved. If you take your origin to be the height at which the projectile is launched, then the projectile at the beginning would have no potential energy but would have kinetic energy. At the peak, it wouldn't be moving and so wouldn't have kinetic energy but would have potential energy. Since energy must be conserved, those are equal.
Remember, in physics, there are often many ways to find the same answer. Your way is right also, but harder (to me).