Aboy throws a ball up into the air with a speed of 8.2 m/s. the ball has a mass of 0.3 kg. how much gravitational potential energy will the ball have at the top of its flight? (assume there is no air resistance

We can use the law of conservation of energy to solve the problem.

The total mechanical energy of the system at any moment of the motion is:

where U is the potential energy and K the kinetic energy.

At the beginning of the motion, the ball starts from the ground so its altitude is h=0 and therefore its potential energy U is zero. So, the mechanical energy is just kinetic energy:


When the ball reaches the maximum altitude of its flight, it starts to go down again, so its speed at that moment is zero: v=0. So, its kinetic energy at the top is zero. So the total mechanical energy is just potential energy:

But the mechanical energy must be conserved, Ef=Ei, so we have

and so, the potential energy at the top of the flight is