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image Suppose we have a frictionless surface and a small particle of mass $m$ which collides with velocity of $V$ with stationary particle of $2m$ elastically. I know how to deal with this simple problem here but I have got a confusion regarding coefficient of resistitution equation . Firstly I wrote equation of linear momentum conservation $$mV=2mV_1 + mV_2$$ Now I can conserve kinetic energy but I want to write other equation using resistitution coefficient(after all I can avoid squares ) $$e=\frac{v_{separation}}{v_{approach}}$$ Now here $e=1$(elastic collision ) So what will be second equation ? $$V=V_2-V_1$$ Or $$V=V_1-V_2$$ This is confusing me too much

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The coefficient of restitution $e$ is defined in a way that $$-ev_{app}=v_{sep}$$ where $v_{app}$, $v_{sep}$ are relative velocities of approach and seperation respectively.

From this, you get, $-eV=V_2-V_1$ and consequently, (since $e=1$ for elastic collisions), $V=V_1-V_2$.

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