A $7\mathrm{.}0$ kg mass $($m$1)$ sits at the top of a frictionless hill. It is up against a very long spring withspring constant k $=140$ N that has been compressed $2\mathrm{.}0$ m$.$ The spring is released and pushesm$1$ forward. mi slides down the hill.a$)(13$ points$)$ Determine the speed of mi just before it hits mass mr$.$b$)(8$ points$)$ mi has a collision with mass mz$.$ After the collision, mi goes backwards $($to the left$)$ with a speed equal to $$ what it was just before the collision $($your answer to parta$).$ Determine the speed of mz after the collision.$(13$ points$)$ mz goes off to the right, up a frictionless slope $($vertical height $2$ m$)$ to a levelsurface. As soon as it levels off, the ground suddenly develops friction $($uk $=0\mathrm{.}3).$ At thesame time, a reverse thruster turns on$,$ giving mz a force of $40\mathrm{.}0$ N to the left. How far after the thruster turns on does m$2$ go before it comes to a stop?