Determine the distance $\backslash ($ s $\backslash )$ to which the $63-$kg painter can climb without causing the $4\mathrm{.}7-$m ladder to slip at its lower end $\backslash ($ A $\backslash ).$ The top of the $\backslash (19-\backslash$mathrm$\{$kg$\}\backslash )$ ladder has a small roller, and at the ground the coefficient of static friction is $0\mathrm{.}31.$ The mass center of the painter is directly above her feet.

Assume $\backslash ($ L$=4\mathrm{.}7\backslash$mathrm$\{$~m$\},$ a$=1\mathrm{.}68\backslash$mathrm$\{$~m$\}\backslash ).$