A ball rolls up a ramp which abruptly ends with the ramp dropping straight down.

Question

A ball rolls up a ramp which abruptly ends with the ramp dropping straight down. The ball launches off the end of the ramp while still traveling at an upward trajectory, goes through projectile motion, and returns to the same height as the base of the ramp. Ignoring any slowing friction (rolling friction), when the ball returns to the height of the ramp's base, the ball lands with a greater speed than when it entered the ramp. why?

I got the basis that the rotational energy gets converted to translational energy but I would like futher understanding on this concept....

Explanation / Answer

You don't really need to worry about rotational energy at all in this question. When a projectile is launched from a certain height H at a speed of v0, when it comes back down to the height H, it will now have a speed of -v0. In this case, the ball is landing at a lower height than the top of the ramp. This allows for more acceleration of the ball due to gravity and a larger vertical component of velocity downwards. So when we find the overall velocity vector, it is larger than the initial velocity when the ball leaves the top of the ramp.

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