$5.$ A $15$ kg stone slides down a snow covered hill leaving point A with a speed of $10$ m$/$s$.$ There is no friction on the hill between points A and B$,$ but there is friction on the level ground at the bottom of the hill, between B and the wall. After entering the rough horizontal region, the stone travels $100$ m and then runs into a very long, light spring with a force constant k $=2\mathrm{.}00$ N$/$m$.$ The coefficient of kinetic and static friction between the stone and the horizontal ground are $0\mathrm{.}2$ and $0\mathrm{.}8$ respectively. a$.)$ What is the speed of the stone when it reaches point B$?$ b$.)$ How far will the stone compress the spring? c$.)$ Will the stone move again after it has been stopped by the spring?