Question

derive simple potential energy

Answer 1

consider an object of mass, m be raised to a height, h from the ground. A force is required to do this. The minimum force required to do this is equal to the weight of of the object, mg. The object gains energy equal to the work done on it. Let the work done on the object against the gravity (as moving upwards)  be W. that is,

work done W = force * displacement
                      =    mg * h
                      =    mgh 
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Answer 2

poteintial energy is energy which is gained by a objet when it moves.
during freefall the heighest poteintial energy would be before striking