A length L $=14\mathrm{.}0-$m uniform ladder weighing wL $=510\mathrm{.}0$ N rests against a wall; there is no friction between the

ladder and the wall. The ladder makes angle $=35\mathrm{.}0$ with the vertical wall.

$($a$)$ Find the horizontal and vertical forces $($in N$)$ the ground exerts on the base of the ladder when a

firefighter of weight wF $=840\mathrm{.}0$ N has climbed distance d $=4\mathrm{.}20$ m along the ladder from the bottom.

$($b$)$ If the ladder is just on the verge of slipping when the firefighter is distance b $=9\mathrm{.}10$ m from the bottom,

what is the coefficient of static friction between ladder and ground?

$=0\mathrm{.}415$

$($c$)$ Oil is spilled on the ground, causing the coefficient of static friction to decrease by a factor of $2\mathrm{.}4$: oil $=$

$($where is the value from part $($b$)).$ What is the maximum distance $($in m$)$ the firefighter can climb

along the ladder from the bottom before the ladder slips?