$(25)2.$ The $100-$ lb boy at A is suspended from the cable that passes over the quarter circular cliff rock and is held by a $185-1b$ woman. The coefficient of static friction between the cable and rock is $s=0\mathrm{.}2,$ and between the shoes of the woman and the ground is $s^{\text{'}}=0\mathrm{.}8.$

a$)$ Determine the tension of the rope at the woman's hands.

b$)$ Determine if the woman can hold the boy from falling $($must show mathematical proof$).$