Draw a diagram, as above.

The incoming disk (blue), with centre C and radius $R$, enters from the left moving horizontally. The outgoing disk (grey), with centre A and radius $r$, is initially stationary.

The **impact parameter** is the distance between the centres A and C measured perpendicular to the direction of motion BA - ie it is distance CB. Here the impact parameter equals the radius $R$ of the incoming disk and BA is horizontal.

The stationary disk moves off at $45^{\circ}$ to the direction AB (red arrow). Assuming that there is no friction during impact, the impulse forces between the disks are purely normal to the contact surface. The change in momentum of disk A is along the line of their centres CA at the moment of impact. Since disk A was initially stationary, CA is also the direction in which A moves after the collision.

Note that the relative mass of disk A has no effect on its final **direction** but it does affect the final **speed** of disk A. This is because A had no initial momentum, so its final momentum is in the direction of the impulse. Whereas for disk C there was some initial momentum so the final momentum is not in the direction of the impulse.

From the geometry of the triangle ABC you can work out the relation between the two radii $R$ and $r$.

edited Jun 24, 2018 by sammy gerbil