A 2kg ball is thrown upward with a velocity of 15m/s. What is the potential energy of the ball when it gets to its maximum height just before falling back to the ground

Calculation of kinetic energy = 0.5x mass x velocity squared

0.5 x 15sqaured x 2 = 225J is the kinetic energy

the gravitational potential energy is equal to kinetic so it would also be 225J

when rearranging this into a gravitational potential energy formula we find that the maximum height of the ball is 1.5meters.

So at the balls maximum height it would have 225J of gravitational potential energy and 0J kinetic energy and just before it hits the ground it’ll have 225J of kinetic and 0J of gravitational potential energy. This is why the rule of:
lost gravitation = gained kinetic is valid.

If its history of, then b) because a) implies only present day (now)