Conservation of Energy by a Rolling Sphere

[lapo3399]

Homework Statement

A rolling ball traveling horizontally with a certain initial translational velocity comes to a hill with a defined height. Upon reaching the top, it flies off of a cliff and falls to the ground and ends up at the same relative height that it began at. If the final diagonal velocity upon hitting the ground is greater than the initial horizontal velocity, has the ball gained energy? Explain.

2. The attempt at a solution
It is impossible for the ball to have gained overall energy, as the sum of kinetic and potential energy is always maintained. In this case, kinetic energy includes rotational and translational energy. I do not understand what has happened exactly, however, as the change in potential energy must be zero as the height did not change overall, so the total change in velocity must be solely attributed to kinetic energy. This means, however, that energy emerged from somewhere, which does not make sense. I guess this could have something to do with conservation of momentum, but I am not exactly sure how.

 

[catkin]

What is "diagonal velocity"? What sort of English is "it flies off of"? Is this the full problem as set or has it been paraphrased?

 

[Astronuc]

Roll a ball up an incline and what happens? What happens to the motion - translational and rotational?