= Collision contact geometry is not determined by incoming velocities
{title2=$\mathbf J\parallel\mathbf n$}
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 $(\sqrt3w/2,w/2)$, and outgoing first <velocity> $(0,h)$, <conservation of momentum> and conservation of <kinetic energy> give $w(\sqrt3u+h)=2u^2+4h^2$. Thus specifying only the first outgoing $x$ component leaves a family: $h=0$ gives $w=2u/\sqrt3$, while $h=u/\sqrt3$ gives $w=5\sqrt3u/6$.
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