Briefly describe the relative quantities of kinetic, gravitational potential and mechanical energy as a stone is thrown in the air vertically upward and falls to the person's hand at the same height that it left.

Answer 1

KE = (1/2)*m*v^2
PE = m*g*h
ME=KE+PE

initially from rest:
Everything is 0

As it leaves from rest, and reaches maximum height, PE increases (because from the formula, h increases)

When it reaches max height, for a moment, the stone will stop in the hair for a short time before coming down, and when this happen, velocity is 0 which means KE decreases

From conservation of energy, ME will be the same

So in short:

As the stone rises in height, the kinetic energy decreases and the potential energy increases. The mechanical energy will be the same.

Answer 2

as it leaves the hand, ME = (1/2)mv^2 and mgh = 0