$(1)(25$ points$)$ A box with a mass of $10\mathrm{.}0$ kg starts from rest at the top of a $15\mathrm{.}0$ m high frictionless ramp. The box slides down the ramp and reaches a flat, horizontal surface. On this surface, the coefficient of kinetic friction between the box and the surface is $0\mathrm{.}25.$

$($a$)$ What is the speed of the box as it

arrives at the hattom of the ramp?

$($b$)$ How far does the box travel along the horizontal surface before coming to rest?