 Solution

A totally inelastic collision in the sticking sense has zero final relative velocity, so $q=0$. Both velocities are the conserved centre-of-momentum frame velocity:Thus the bodies move together along the original incident direction; the moving projectile has ${\theta }_1=0$. The common outgoing state is stationary in the centre-of-momentum frame. The lost translational kinetic energy iswhich can become internal energy. As explained in part 8, setting only the normal coefficient of restitution to zero in a smooth oblique collision does not force sticking: tangential relative motion can remain.