In general colliding particles strike each other at an angle and change direction bt anything between 0 and 180 degrees. We take account of this by applying the law of conservation of momentum in two perpendicular directions – usually taking one of these as the direction of the initial velocity of one of the particles - and forming simultaneous equations using the principle of conservation of momentum and the law of restitution.
Applying the Law of Conservation of Momentum horizontally gives
and applying the Law of Conservation of Momentum vertically gives
Now apply the Law of Restitution. The velocities of
and
are
and
respectively.
so
This expression simplifies to
To solve these equations we need another equation, or a condition since we have four unknowns –
if
andare given.