Question $1$: A $5$kg block is set into motion up an inclined plane with an initial speed of $20\frac{m}{s}$ as in the figure. The block comes to rest after traveling $15m$ along the plane, which is inclined at an angle of $37$ to the horizontal and has a coefficient of kinetic friction ${}_k.$

NOTE: The gravitational acceleration is $9\mathrm{.}8\frac{m}{s^2}.$

a$)$ Draw the free body diagram for the block. $(18$ p$)$

b$)$ Find the value of the coefficient of kinetic friction ${}_k.(42$p$)$