Help is needed with physics of billiards

[balingwhale]

Homework Statement

three billiard balls are arranged in an equilateral triangle formation labeled A, B, and C. the impulse which the cue imparts to the cue ball is a given, J, the angles at which the three balls will travel(depart from the stationary arrangement) can be easily found. i won't get into more details until i see someone has acknowledged this post. my question is, is it possible to find the velocities with which each ball "departs" (for lack of a better word).

Homework Equations

using J = delta p i am able to find that ... (see #3)

The Attempt at a Solution

|(v_A ) ⃑ |=1/m |J ⃑ |-2|(v_C ) ⃑ |cosθ
and
|(v_B ) ⃑ |=|(v_C ) ⃑ |

please NOTE: theta is given (or can be found as mentioned above because of the nature of the arrangement)

 

[nvn]

How many equations exist, and how many unknowns do you have?

 

[balingwhale]

breaking up impulse into components on the one side of the equal sign and final momentum into components (the sum of final momentums for each ball.. mv_A + mv_B +mv_C) on the other side of the equal sign will give us 2 equations. there are 3 unknowns. mass, impulse, angle theta are all given. are there any other equations i could use assuming the impact is ideal. can i incorporate conservation if kinetic energy in any way. i don't think so but looking at it i feel that i should be able to find the magnitudes of velocities.

 

[nvn]

balingwhale: Your statements in post 3 are correct. And yes, you can use conservation of energy. Very good. Try it.