Problem $6$:

A $4\mathrm{.}20-kg$ block is set into motion up an inclined plane with an initial speed of $v=8\mathrm{.}20\frac{m}{s}($see figure below$).$ The block comes to rest after traveling $d=3\mathrm{.}00m$ along the plane, which is inclined at an angle of $=30\mathrm{.}0$ to the horizontal.

For this motion, determine the force of kinetic friction exerted on the block. $($Assume that this force of kinetic friction is constant.$)$

$($A$)26\mathrm{.}5$ N

$($B$)61\mathrm{.}7$ N

$($C$)45\mathrm{.}7$ N

$($D$)55\mathrm{.}3$ N

$($E$)65\mathrm{.}6$ N