$(14$ pts$)$ On in frictionless table, a $3\mathrm{.}0$ kg mass maving $4\mathrm{.}0\frac{m}{s}$ to the right collides with an $8\mathrm{.}0$ kg mass moving $1\mathrm{.}5\frac{m}{s}$ to the lett. If the two masses make an elastic, head$-$on collision, what are their final walacities?

mivii $+m_2{v}_{2}i=m,v_{1}f+m_2{J}_{2}f$

$3\mathrm{.}0(4\mathrm{.}0)+8\mathrm{.}0+1\mathrm{.}5$

$0(4)=3\mathrm{.}0vf+8\mathrm{.}0v_{2}f$

$v_{1}f=8\mathrm{.}0\frac{m}{s}$

$v_{2}f=3\mathrm{.}0\frac{m}{s}$