# Resultant velocities from 2D collision

1. Jul 3, 2012

1. The problem statement, all variables and given/known data
Suppose you have two 2D circles, where size ≈ mass, each of which is moving with known x- and y-velocities. The two collide, not necessarily head-on (one could broadside the other, etc). How do I calculate the resultant velocities, assuming no elasticity or friction?

2. Relevant equations
ρ = mv
m1v1 + m2v2 = m1v1 + m2v2
Speed = Square root of (X-velocity^2 + Y-velocity^2)

3. The attempt at a solution
Each circle is moving in a particular angle (direction), and hits the other at a particular angle. If the difference between angles is 0, then the mower transfers all of its momentum to the other. If the difference is approaching 90 degrees, then the amount transferred is approaching 0.

I apologize if this has already been answered; I couldn't find it.
Thanks!

2. Jul 3, 2012

### Yukoel

What do you mean by size ≈ mass?And what is the constraint "no elasticity"?Do you mean that the balls are identical and the collision is assumed to be elastic without any non conservative forces? If yes try to resolve the velocities along the center to center line of spheres at the time of impact.You will be done.
regards
Yukoel

3. Jul 4, 2012

Yukoel,

I'm making a program in which objects, represented by circles, are moving around on the screen. When they hit each other, a collision function is called - the size of the circle is the same as its mass; e.g. circles of radius 70 units have half the mass of circles of radius 140 units. For ease of use, lets say the units are meters, and convert nicely to kilograms; the speeds are in m/s.
I'm unfamiliar with the concept of elasticity (my recent college courses just dealt with head-on collisions with either negligible or a specific amount of friction). In here, there are no non-conservative forces.

I'm sorry, but what do you mean by resolving "the velocities along the center to center line of spheres at the time of impact?"

Thanks,

Edit: A little more information: I checked http://en.wikipedia.org/wiki/Elastic_collision#Two-_and_three-dimensional but I don't quite understand if it's explaining the situation for the second particle being at rest, or more generally.

Last edited: Jul 4, 2012
4. Jul 4, 2012