PROB. $12\mathrm{.}230$

$12\mathrm{.}230$ Two automobiles collide head$-$on$.$ Vehicle A has a mass of $1200$ kg

and an initial speed of $3\frac{m}{s},$ and vehicle $B$ has a mass of $1500$ kg

and an initial speed of $2\frac{m}{s}.$ The coefficient of restitution is $0\mathrm{.}20.$

Determine $($a$)$ the velocities of the two vehicles following the

collision, and $($b$)$ the amount of mechanical energy dissipated by

the collision.