A20 kg ball is thrown into the air. it is going 5.0 m/s when thrown. how much potential energy will it have at the top

When the ball leaves your hand, it has kinetic energy.

              Kinetic energy = (1/2) (mass) (speed)²

                                     = (1/2) (20kg) (5 m/sec)²

                                     =  50 joules .

If the ball is not carrying solar panels or a jet engine, then it can
never have any MORE energy than that.  And if, as we always
assume, it doesn't suffer any air resistance, then it won't LOSE
any energy. It has 50 joules of energy, permanently or until it hits
something.

If you toss it straight up, then it keeps climbing until it runs out of
kinetic energy.  That is, its kinetic energy gets converted to potential
energy as it goes higher and slower.  At the top, where it stops
momentarily and has no kinetic energy at all, all the energy it has
is potential energy ... the entire 50 joules you gave it with your toss.                       

The objects do not reach terminal velocity         there is not enough time from the time the object falls from when it hits the ground to achieve terminal velocity. an object must be placed higher to achieve terminal velocity in order to be in free fall.

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