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Orbiting Billiard Balls

Age 14 to 16 Challenge Level:

At what angle must the billiard ball be struck for it to return to its start position?

Your answer will depend on the length and breadth of the table, but does it depend on where the ball is to start with?

Billiard Table

Don't be too quick to accept this diagram - what assumptions might it be useful to make about the rebound angles?

Now use that to draw your own diagram.