i. Suppose a particle of mass mi moving with initial velocity \(\overrightarrow{u}_1\), undergoes a non head-on collide with another particle of mass m2 and initial velocity \(\overrightarrow{u}_2.\)
ii. Let us consider two mutually perpendicular directions: Common tangent at the point of impact, along which there is no force (or no change of momentum).
Line of impact which is perpendicular to the common tangent through the point of impact, in the two-dimensional plane of initial and final velocities.
iii. Applying the law of conservation of linear momentum along the line of impact, we have,
m1u1 cos α1 + m2u2 cos α2 = m1v1 cos β1 + m2v2 cos β2
As there is no force along the common tangent,
m1u1 sin α1 = m1u1 sin β1 and m2u2 sin α2 = m2v2 sin β2
iv. Coefficient of restitution (e) along the line of impact is given as
