9.3 For oblique collision

1.1 Position of centre of mass for a system of two particles

2.1 Rod
2.2 Semicircular ring
2.3 Semicircular disc
2.4 Solid sphere
2.5 Hemispherical Shell
2.6 Rectangular Plate
2.7 Square Plate
2.8 Circular Plate
2.9 Solid Cone
2.10 Hollow Cone
2.11 Questions
2.12 Centre of mass of a rigid complex bodies

3.1 Motion of mass of the system

5.1 Rocket Propulsion

6.1 Instantaneous impulse

9.1 For direct collision
9.2 For collision in two dimension
9.3 For oblique collision

10.1 Head on elastic collision
10.2 Head on inelastic collision

Coefficient of restitution $(e)$ is given as, $$e = \frac{{{v_{{2_{CN}}}} - {v_{{1_{CN}}}}}}{{{u_{{1_{CN}}}} - {u_{{2_{CN}}}}}}$$

So for oblique collision, component of the velocity along the common normal will be taken.

Therefore for the given example, coefficient of restitution is, $$\begin{equation} \begin{aligned} e = \frac{{{v_{{2_{CN}}}} - {v_{{1_{CN}}}}}}{{{u_{{1_{CN}}}} - {u_{{2_{CN}}}}}} = \frac{{{v_2} - \left( { - {v_1}\sin \theta } \right)}}{{{u_1}\sin \theta - \left( { - {u_2}\cos \theta } \right)}} \\ e = \frac{{{v_2} + {v_1}\sin \theta }}{{{u_1}\sin \theta + {u_2}\cos \theta }} \\\end{aligned} \end{equation} $$

Note: The above derived coefficient of restitution $(e)$ is only for the above example. For different oblique collision different value of $e$ is obtained.