Given a circular billiards table with center O,
radius r, and no pockets. A cue ball (with a
radius negligible compared to r) is placed at
point A such that 0<|OA|≤r. The ball is struck
and bounces off the cushion twice before
returning to point A.
How was the direction of the shot determined?
(In reply to
re: Obvious?? by Kenny M)
(I failed to enter a few words in my text, which I've now added but I don't think that was a concern).
Quote from comment: ".... return to its rest twice if its path is directly over the the central
point and struck firmly enough. The points of contact will be at
tangents...."
For the ball to pass over its initial point of rest twice it must travel the length of the diameter at least twice, to one tangent and rebound from the other.
The problem text mentions two contacts with the cushion but does not exclude passing over that location, just being there at the journey end. As this problem is designated D3 then such a solution as this would hardly be D1, and so was obviously not in Bractals' thoughts.
The latter part of that comment does describe what I believe he wants but does lack the "precision" of a mathematical formula - which is probably required.
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Posted by brianjn
on 2013-04-23 23:04:34 |
re(2): Obvious??
