Final answer:
In an idealized scenario with conservation of mechanical energy, a ball with initial velocity 7.2 m/s rolling up a hill without slipping will stop and roll back down once its kinetic energy is fully converted to potential energy.
Step-by-step explanation:
The fate of a ball with an initial velocity of 7.2 m/s rolling up a hill without slipping is that it will come to a complete stop and then roll back down (option A). The reason for this outcome is due to the conservation of mechanical energy, which encompasses both kinetic energy when the ball is in motion and potential energy when it gains altitude. As the ball rolls uphill, its kinetic energy is gradually converted into gravitational potential energy until all the kinetic energy has been expended in raising its height. Upon reaching this point, the ball has zero kinetic energy, and thus it stops for a brief moment before rolling back down the hill. Ignoring other forms of energy, such as rotational kinetic energy or any losses due to friction or air resistance, this answer assumes an idealized scenario where mechanical energy is conserved. However, if there is no additional external force to keep the ball at the top, it cannot stay there; as soon as it stops, gravity will pull it back down.