After some time searching, I have revised my question.
I have found numerous examples of ball to ball collisions, but the only ones that seem to work use Vector2d or Vector2D.
This is a problem, because I am only allowed to use the regular java library, so my main question is: How do I convert the examples (which I will post below) to use what I can use?
I have several variables, both balls have the same mass, the velocities are broken into different variables, x and y. Also I have access to their x and y pos.
This is the ONLY problem left in my application.
I am at a total loss on how to convert the below example.
// get the mtd
Vector2d delta = (position.subtract(ball.position));
float d = delta.getLength();
// minimum translation distance to push balls apart after intersecting
Vector2d mtd = delta.multiply(((getRadius() + ball.getRadius())-d)/d);
// resolve intersection --
// inverse mass quantities
float im1 = 1 / getMass();
float im2 = 1 / ball.getMass();
// push-pull them apart based off their mass
position = position.add(mtd.multiply(im1 / (im1 + im2)));
ball.position = ball.position.subtract(mtd.multiply(im2 / (im1 + im2)));
// impact speed
Vector2d v = (this.velocity.subtract(ball.velocity));
float vn = v.dot(mtd.normalize());
// sphere intersecting but moving away from each other already
if (vn > 0.0f) return;
// collision impulse
float i = (-(1.0f + Constants.restitution) * vn) / (im1 + im2);
Vector2d impulse = mtd.multiply(i);
// change in momentum
this.velocity = this.velocity.add(impulse.multiply(im1));
ball.velocity = ball.velocity.subtract(impulse.multiply(im2));
Here is the URL for the question:
http://stackoverflow.com/questions/345838/ball-to-ball-collision-detection-and-handling
And I have taken a look at his source code.
Thank you for taking the time to read this issue.
SUCCESS!
I have found how to use Vector2d, and it works PERFECTLY! Will edit later with answer!