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Weekly Challenge 13: Comet Catastrophe

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

Pool Shot

Stage: 5 Short Challenge Level: Challenge Level:2 Challenge Level:2

Suppose we have a pool table without pockets and with side lengths $a$ and $2b$. The ball is placed at point A.

1) Find four different angles for the ball to get back to the same point A.

2) Find four possible angles for the ball to go to the point D.

 


 


3) This is a bit more challenging question. Find four different angles in each situation 1) and 2) if we have the same pool table but with pockets. The ball starts to move from the point A which is just in front of the pocket.

State any assumptions that you make.