A mass, m$\_(2),$ is initially at rest. A mass, m$\_(1),$ traveling with velocity, v$\_(1),$ collides with m$\_(2)$ in an

elastic collision. After the collision, the two objects move with final velocities,

u $\_(()1$f$)$ and

u $\_(()2$f$)$ respec$-$

tively. Using the laws of conservation of energy and momentum, show that the ratio of the final

velocities in terms of m$\_(1)$ and m$\_(2)$ is given by:

$($v$\_(1$f$))/($v$\_(2$f$))=($m$\_(1)-$m$\_(2))/(2$m$\_(1))=-(1)/(2)($m$\_(2))/($m$\_(1))+(1)/(2)$