Question

You throw a softball (of mass 350 g) straight up into the air. it reaches a maximum altitude of 13.5 m and then returns to you. what is the gravitational potential energy of the softball at its highest position? assume the ball departed from and returned to ground level. answer in units of j.

Answer 1

GPE = mgh Where m is the mass of the object (kg), g is acceleration due to gravity (which I will assume to be 9.81ms-2), and h is the height of the object above ground level. This is used in cases where the object is close to the earth, since any change in gravitational force is negligible.

Substituting in the numbers:
$GPE=0.35*9.81*13.5=46.35 \\ \boxed{=46.4J \ \ to \ 3sf}$

Answer 2

It doesn't matter where the ball started from, or where it returned to,
or what direction you tossed it, or what happened to it before or after
it reached its highest altitude, or whether somebody shot it down, or
whether it landed in a mud puddle, or what its highest altitude was. 

The gravitational potential energy of the ball only depends on its mass,
its altitude, and the acceleration of gravity.

          Potential energy = (mass)  x  (gravity)  x  (height)

                                       = (0.35 kg) x (9.8 m/s²) x (13.5 m)

                                       =    46.3 kg-m²/s²

                                       =     46.3 Joules