How to calculate the direction (of velocity of a ball) after collision with another ball?

Question

Say I have two balls of same radius, in the 2-D Plane. So like a pool (billiard) game. I have the cue ball, moving with the velocity vector V, the magnitude is not important, so we only need an angle to define the velocity, which is theta.

Depending on theta and r, the balls may or may not collide. So let's say we know that they will collide, and we know the initial positions, radii, as well as theta. So how do we calculate the angle of movement of the second ball ?

I hope the picture helps if I failed to define the problem.

P.S.

Although I stated the problem with theta, I'm also ok with a vector-form solution.

Answer 1

When they collide, the point of impact between the two is along a plane (you can imagine a straight line between the two at impact) The resulting direction of the target ball is perpendicular to that plane. AKA The direction of the target ball is along the line of the center of the cue ball, to the center of the target ball.

(This isnt from my math, this is from my experience in playing pool)

Answer 2

It depends on exactly where on the Target the Cue hits. Assuming the simplest case - no friction, etc - the Cue will deliver an impact along the line of centres at the moment they hit, so that the Target will move off along that line.