Propose a hypothesis for how the position of the ball will affect the amount of its gravitational pull energy

throwing a ball up initially has a lot of kinetic energy because it is moving upwards (kinetic energy is energy which a body possesses by virtue of being in motion.) this all then get converted to gravitational potential energy, and for a moment it is stationary before it begins to fall again. by the time it has returned again, all the gravitational potential energy has turned back into kinetic.