The Pocket Ball

On a billiard table A B C D ABCD with integer side lengths, a ball is shot from point A A at an angle of 3 0 30^\circ with side A D . AD.

Which pocket will the ball eventually go into?

(The ball falls only when the center of the ball and the corner point hit match exactly. Also, disregard any friction or air resistance.)

A B C D None of them

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1 solution

Pepper Mint
Oct 7, 2017

The ball's horizontal distance:vertical distance is 1 : 3 1:\sqrt{3} . However, since every side has integer length, they can never make the proportion 1 : 3 1:\sqrt{3} . Thus, the ball cannot get in any holes.

I agree with the solution: I did it the same way. However, I think the question needs more clarification that the ball never slows down, there is no spin on the ball etc.

Stephen Mellor - 3 years, 8 months ago

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OK, I've specified it in the problem. Thanks.

Pepper Mint - 3 years, 8 months ago

The way I thought about it was imagining an infinite number of tesselating pool tables, and at each reflection, the ball continues in a straight line to the adjacent table.

Joe Mansley - 2 months ago

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