Determine the minimum coefficient of static friction between the $4$ m ladder and the ground such that the ladder will not slip at its lower end A$.$ The $44\mathrm{.}1$ kg painter stands at a distance$$s $=3\mathrm{.}23$ m from the bottom end of the ladder. The top of the $11\mathrm{.}2$ kg ladder has a small roller.$$ Assume

$(1)$ The mass centre of the painter to be directly above her feet,$$

$(2)$ There is no friction between the small roller on top of the ladder and the wall.

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