physics projectile problem with max height

Question

A projectile of mass 0.5 kg is shot straight up with an initial speed of 18.8 m/s. How much energy is lost from the system if it reaches a max height of 15.9048 meters? 

Answer 1

If no energy is lost, the energy at maximum height should be

mv²/2 = (0.5)(18.8)²/2 J = 88.36 J

That should equal mgh_max.

mgh_max = (0.5)(9.8)(15.9048) J = 77.93 J

The energy lost is the difference between these two values.