= Laboratory scattering circle
{title2=$|\mathbf v_1'-\mathbf V|=qM_2u_1/(M_1+M_2)$}
When a particle of <mass> $M_1$ and initial <speed> $u_1$ strikes a stationary <mass> $M_2$, the <centre-of-momentum frame> moves at $\mathbf V=M_1u_1\widehat{\mathbf x}/(M_1+M_2)$. If the <relative speed retention in an oblique collision> is $q$, its possible outgoing <velocity> vectors lie on the displayed circle in a scattering plane. Intersect a ray of fixed laboratory direction with that circle to obtain the quadratic formula for outgoing <speed>. A negative root is inadmissible, and the origin has no defined <scattering angle>. Tangency gives the maximum laboratory angle when the circle excludes the origin.
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