A projectile of mass m leaves the ground with a kinetic energy of 220 J. At the highest point in its trajectory, its kinetic energy is 120 J. To what vertical height, relative to its launch point, did it rise?

The work-energy principle:  The net work done on an object is equal to the change in the object's kinetic energy.

The principle of conservation of mechanical energy for conservative forces: If only conservative forces are acting, the total mechanical energy of a system neither increases nor decreases in any process. It stays constantπit is conserved.
The law of conservation of energy: The total energy is neither increased nor decreased in any process. Energy can be transformed from one form to another, and transferred from one object to another, but the total amount remains constant.