$8.(10$ points$)$ Car A$,$ of mass $1100$ kg$,$ is stopped at a traffic light when it gets rear$-$ended

by car B$,$ of mass $1400$ kg$.$ Both cars then slide with locked wheels until friction from

the road stops them. The road is slick, with k $=0\mathrm{.}13.$ Car A slides $8\mathrm{.}2$ m while car B

slides $6\mathrm{.}1$ m$.$

$($a$)(3$ points$)$ What is the speed of car A$,$ immediately after the collision and before it

slides an appreciable distance?

$($b$)(2$ points$)$ What is the speed of car B$,$ immediately after the collision and before it

slides an appreciable distance?

$($c$)(3$ points$)$ Assuming that momentum is conserved during the collision, find the

speed of car B just before the collision.

$($d$)(2$ points$)$ Explain why the assumption of conservation of momentum may not be

valid.