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Circular Billiards Table (Posted on 2013-04-23) Difficulty: 3 of 5

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?

See The Solution Submitted by Bractals    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Playing with Geometers' Sketchpad | Comment 4 of 6 |
(In reply to re(2): Obvious?? by brianjn)

I think what's wanted is a relation such as:

When |OA|/r = .9, the angle of the shot with the ray to the center is 32.4.

When |OA|/r = .75, the angle of the shot with the ray to the center is 36.8.

When |OA|/r = .5, the angle of the shot with the ray to the center is 47.1.

with some sort of functional ralationshipe between |OA|/r and the required angle.

The numbers are approximations derived from moving the first point of reflection along the circle while seeing the ray after the second reflection off the circle go through various locations of the initial point.

  Posted by Charlie on 2013-04-23 23:21:21
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