Question

Two particles of masses $m$ and $2m$ moving in opposite directions collide elastically with velocity $2\nu$ and $\nu$ respectively. Find their velocities after collision.

Answer 1

Let the final velocities of $M$ and $2m$ bc ${\nu }_1$ and ${\nu }_2$respectively, as shown in Fig.
By conservation of momentum, we get
$m\left(2\nu {)}_{2}m\right(-\nu )=m({\nu }_1)+2m({\nu }_2)$
or $0=m{\nu }_1+2m{\nu }_2$
or ${\nu }_1+2{\nu }_2=0$

and since the collision is elastic,
${\nu }_2-{\nu }_1=2\nu -(-\nu )$
or ${\nu }_2-{\nu }_1=3\nu$
Solving the above two equations, we get
${\nu }_2=\nu$ and ${\nu }_1=-2\nu$
That is, mass $2m$ returns with velocity $\nu$ while mass $m$ returns with velocity $2\nu$ in the direction shown in Fig.