= 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>:
$$
\boxed{\mathbf v'_1=\mathbf v'_2=\frac{M_1u_1}{M_1+M_2}\widehat{\mathbf x}.}
$$
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> is
$$
\Delta K=\frac12\frac{M_1M_2}{M_1+M_2}u_1^2,
$$
which can become internal <energy>. As explained in part <8>, setting only the normal <coefficient of restitution> to zero in a smooth <oblique collision> does \b[not] force sticking: tangential relative motion can remain.
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