Question

Jeanette is playing in a 9-ball pool tournament. She will win if she sinks the 9-ball from the final rack, so she needs to line up her shot precisely. Both the cueball 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 the 9-ball off center, so that when theballs collide, they move away from each other at the same angle theta from the direction in which the cue ball was originally traveling (see figure). Furthermore,after the collision, the cue ball moves away at speed v_f, while the 9-ball moves at speed v_9.

For the purposes of this problem, assume that the collision is perfectly elastic, neglect friction, and ignore the spinning of the balls
Find the angle theta through which the 9-ball travels away from the horizontal, as shown in the figure. Perhaps surprisingly, you should be able to obtain anexpression that is independent of any of the given variables!
Express your answer in degrees to three significant figures.
theta =


rm degrees

Answer 1

If you set up this problem, knowing that it is perfectly elasticmeans that conservation of momentum and conservation of kineticenergy are observed.

So, you get:

p_i = p_f
mv_i = mv_f + mv₉
divide by massto get: v_i = v_f + v₉
You could do some trig substitutions with each x and y component ofmomentum to get some isolated equations, but I thought it waseasiest to move on to the conservation of kinetic energy.

Now, with the kinetic energy you get:
K_i = K_f
1/2 mv_i² = 1/2 mv_f² +1/2 mv₉²
Again, dividing by 1/2 mass toget: v_i²= v_f² +v₉²

This should look like the Pythagorean theorem. Knowing thatthe tail to head method of vectors would also give an image whereyou have a 90 degree angle, then 2θ = 90 => θ = 45^o.

Answer 2

the anser is 44 degrees

Answer 3

sink these balls in ur mouf nigga

Answer 4

The answer is 45, don't let those pricks fool you

Answer 5

Don't listen to them its 46, they are trying to play you hard