Elliptical 1 Ball Pool.
A ball placed on either of the foci of an elliptical pool table eventually moves along the major axis of the table.
Calculate the coefficient of restitution for the collisions.
Assume that all collisions between a ball and the boundaries of the table are identical, i.e. they have the same coefficient of restitution. Also, the ball can be struck at any possible angle.
Bonus: Find the shape of the table such that the probability of a ball going into a particular hole is maximized (for a perfectly elastic collision).
The answer is 1.
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