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23 Nov 2019

Jeanette is playing in a 9-ball pool tournament. She will win ifshe sinks the 9-ball from the final rack, so she needs to line upher shot precisely. Both the cue ball and the 9-ball have mass m ,and the cue ball is hit at an initial speed of v_i. Jeanettecarefully hits the cue ball into the 9-ball off center, so thatwhen the balls collide, they move away from each other at the sameangle theta from the direction in which the cue ball was originallytraveling (see figure). Furthermore, after the collision, the cueball moves away at speed v_f, while the 9-ball moves at speedv_9.

For the purposes of this problem, assume that the collision isperfectly elastic, neglect friction, and ignore the spinning of theballs
Find the angle theta through which the 9-ball travels away from thehorizontal, as shown in the figure. Perhaps surprisingly, youshould be able to obtain an expression that is independent of anyof the given variables!
Express your answer in degrees to three significant figures.
theta =


\rm degrees

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Irving Heathcote
Irving HeathcoteLv2
6 Oct 2019

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