In a railroad switchyard, a

$56$

$-$

ton

freight car is sent at

$7$

$.$

$0$

$$

mi$/$h

toward a

$31$

$-$

ton

car moving in the same direction at

$2$

$.$

$6$

$$

mi$/$h

$.$

$($a$)$ What$$s the speed of the cars after they couple? $($b$)$ What fraction of the initial kinetic energy was lost in the collision?

$.$

Describe the motion of the second piece