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A ladder with a length of $5\mathrm{.}0$ m and a weight of $400$ N is placed so its base is on the ground $4\mathrm{.}0$ m from a vertical frictionless wall, and its tip rests $3\mathrm{.}0$ m up the wall. The ladder remains in this position only because of the static friction force between the ladder and the ground. You, with a weight of $500$ N $,$ are standing on the ladder at a Find the magnitude of the upward normal force applied by is uniformly distributed.

$($b$)$ Find the magnitude of the horizontal normal force applied by the wall on the ladder.

$$ N

$($c$)$ Determine the minimum possible coefficient of static friction for the ladder$-$ground interaction, for the ladder to remain at rest.

$$

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