A rock starts at ground level with 741 joules of kinetic energy and rises until it ceases moving. What is its gravitational potential energy at...

Applying conservation of energy, the initial total kinetic energy is equal to the total final energy. 

Since the rock starts at ground level, its height zero (h=0). So, its potential energy is zero. Thus, the initial total energy consist only of the given kinetic energy.

 

Then, the rock rises until it ceases moving. At this height h,  the velocity of the rock is zero (v=0). So, its kinetic energy is zero. Thus, the final total energy consist only of the potential energy.

Setting the initial total energy and final total energy equal to each other, then the potential energy at height h is:

Therefore, when the rock reaches the point it stops moving, its gravitational potential energy is 741 Joules.