# Two dimensional elastic collisions with varying angle of incident

If in an elastic collision I know all initial values and that mass for each object remains constant throughout the collision (but different from one another) how can I determine their final velocity vectors when the angle of incident is also a variable?

I've tried decomposing the vectors and have determined that for perpendicular collisions the following formula will work:

$$v_1=\frac{u_1(m_1−m_2)+2m_2u_2}{m_1+m_2}.$$

Will this work for variable angles as well?

-

This equation works but for those components of velocities in direction of contact of two bodies i.e in the direction of forces they exert on each other,in the direction perpendicular to the force the velocities won't change.

-

In general, there is no solution to the outgoing velocities of the particles. You need 6 components (three components of velocities for each particles) but you have only 4 equations (three components from the conservation of momentum, one from the conservation of energy). There are 2 equations missing.

To resolve this problem, you have to define what happens microscopically during the collision. For example, you can use a known potential for the interaction between the two particles and derive the trajectories.

-