I was asked this question earlier and was unable to provide a definitive answer because I wasn't sure if the assumption was valid.
The question is asking for what values of $u$ will the ball fall into the hole. From the diagram, the question seems to assume that the condition for the ball to fall in is if the equator of the ball is parallel with the ground.
My problem is that I am skeptical of this assumption and would like to seek further advice on this.
My thoughts currently are:
- The leftmost limit is physically impossible unless the ball is dropped vertically from that position. Otherwise the point of contact is somewhere in the third quadrant of the ball.
- The rightmost limit is possible, but intuition appears to say that it is also possible for the ball to fall in if the point of contact is in the fourth quadrant of the ball
- This whole system doesn't take into consideration the elastic/bounce factor of the ball. If we assume a zero bounce factor, how does that change things?
