Answer:
GE = ME - [tex]\frac{1}{2} m\,v^2[/tex], which agrees with option C in your list.
Explanation:
The definition of Mechanical Energy (ME) of a system is the addition of the gravitational potential energy (GE) plus the kinetic energy (KE) of the system:
ME = GE + KE
Given that the KE is: [tex]\frac{1}{2} m\,v^2[/tex],
solving for GE in the formula above gives:
GE = ME - KE = ME - [tex]\frac{1}{2} m\,v^2[/tex], which agrees with option C
