Problem $4$: $(25\%$ of Assignment Value$)$

A cube of mass m is initially at rest at the top of an inclined plane which has a height of $5\mathrm{.}37$ m and makes an angle of $\backslash$theta $=19\mathrm{.}8\backslash$deg with respect to the horizontal. After

letting go of the object, you notice it to be traveling at v$=6\mathrm{.}22($m$)/($s$)$ a distance d after the end of the inclined plane, as shown. The coefficient of kinetic friction

between the cube and the plane is $\backslash$mu $\_($p$)=0\mathrm{.}10,$ and the coefficient of friction on the horizontal surface is $\backslash$mu $\_($r$)=0\mathrm{.}20.$

Part $($a$)$

What is the speed of the cube, in meters per second, just after it leaves the inclined plane?

v$\_($bottom $)=[,]($m$)/($s$)$

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Part $($b$)$

Find the distance, d$,$ in meters.