Collision contact geometry is not determined by incoming velocities ($\mathbf{J}\parallel \mathbf{n}$)

In a smooth oblique collision, the impulse is parallel to the contact normal $\mathbf{n}$, while tangential velocity components remain unchanged. Incoming velocities, masses, and a coefficient of restitution do not determine the outgoing velocities until that contact normal, or equivalent scattering data, is specified. For an elastic collision of masses $3m,m$, incoming velocities $(-u,0)$ and $(\sqrt{3}w/2,w/2)$, and outgoing first velocity $(0,h)$, conservation of momentum and conservation of kinetic energy give $w(\sqrt{3}u+h)=2u^2+4h^2$. Thus specifying only the first outgoing $x$ component leaves a family: $h=0$ gives $w=2u/\sqrt{3}$, while $h=u/\sqrt{3}$ gives $w=5\sqrt{3}u/6$.