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. Jeanette carefully hits the cue ball into the9-ball off center, so that when the balls collide, they move awayfrom each other at the same angle θ 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 speed v₉.

For the purposes of this problem, assume that the collision isperfectly elastic, neglect friction, and ignore the spinning of theballs.

Find the angle ? that the 9-ball travels away from the horizontal, asshown in the figure.

Express your answer in degrees tothree significant figures.

?=

m m