In an elastic head$-$on collision, a $0\mathrm{.}60$ kg cart moving at $5\mathrm{.}0$ m$/$s $[$W$]$ collides with a $0\mathrm{.}80$ kg cart moving at $2\mathrm{.}0$ m$/$s $[$E$].$ The collision is cushioned by a spring $($k $=1200$ N$/$m$).$

Determine the velocity of each cart after the collision.

Determine the maximum compression of the spring.