Recently on one of the math sites there was some discussion of a recent math
article that claims that the standard math text treatment of pool table
physics is wrong. The standard math text treatment uses a mirror over the
edge of the bumper and has the player aim at the virtual image. However
this is wrong. The mirror must be moved in by about the radius of the ball.
See: www.hal-pc.org/~clement/BoolBallReflection.jpg
for an illustration of the problem. Of course this is assuming an elastic
hard collision model with no friction. The realistic answer will be
somewhat different and should be velocity dependent.
I suspect this has already been discussed or is written up in one of the
physics journals or textbooks. Would anyone have a source for this?