A good way to calculate the sphere collision problem is to convert to the
zero-momentum frame.

If you consider the frame of reference where the total momentum of the
system is stationary, i.e. when the observer is travelling at half the speed
of SB. This observer will see SB moving at a particular speed along the
x-axis and SA moving at the same speed in the opposite direction.

After the collision, the total momentum in this frame still has to be zero,
but the spheres will be moving in different directions, BUT they must be
going at the same speed and in opposite directions to keep the momentum at
zero. Then you just need to add on the speed of the zero-momentum frame to
get the new velocities of the spheres in the normal frame of reference.

The only thing that needs to be worked out now is the angle at which the
spheres change in the zero momentum frame. Since the force between the
spheres at the time of impact is exerted along the line containing the
centers of the spheres, we know the initial speed and direction of motion,
the final speed of motion, and the direction of the force. This is enough
information to calculate the angle by the impulse formula

Ft = d(mv)/dt

-Chris

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