Question

A ball is projected into the air with 100 j of kinetic energy which is transformed to gravitational potential energy at the top of its trajectory. when it returns to its original level after encountering air resistance, its kinetic energy is

Answer 1

when it returns to its original level after encountering air resistance, its kinetic energy is decreased. 
In fact, part of the energy has been dissipated due to the air resistance.

The mechanical energy of the ball as it starts the motion is:
$E=K = 100 J$
where K is the kinetic energy, and where there is no potential energy since we use the initial height of the ball as reference level.
If there is no air resistance, this total energy is conserved, therefore when the ball returns to its original height, the kinetic energy will still be 100 J. However, because of the presence of the air resistance, the total mechanical energy is not conserved, and part of the total energy of the ball has been dissipated through the air. Therefore, when the ball returns to its original level, the kinetic energy will be less than 100 J.