Final answer:
According to the law of conservation of momentum and the work-energy principle, the final kinetic energies can be greater if work is done on a system, even though in inelastic collisions kinetic energy is not conserved. The total mechanical energy can change depending on whether additional energy is added to the system through work.
Step-by-step explanation:
The question pertains to the concept of conservation of energy and how kinetic energy can change in a system. In the context of the provided passages, there seems to be a confusion about how the final kinetic energies can be greater than the initial kinetic energy of the incoming ball. A key point to understand is that while momentum is conserved in collisions, kinetic energy may not be, especially in inelastic collisions where energy is lost to other forms such as heat or sound. However, in situations where work is done on the system, such as by external forces or via gravitational potential energy, the final kinetic energy can exceed the initial kinetic energy.
Considering the law of conservation of momentum, if an external force does work on a system without causing momentum change, it can result in an increase in kinetic energy. An important concept here is that work adds energy to the system, and depending on the type of collision, total mechanical energy can increase or decrease.