A.
In order to calculate the force of kinetic friction, we can use the formula:
[tex]F=N\cdot\mu[/tex]Where N is the normal force and μ is the coefficient of kinetic friction.
Since the floor is horizontal, the normal force is equal the weight, so we have:
[tex]\begin{gathered} N=m\cdot g \\ F=m\cdot g\cdot\mu \\ F=42\cdot9.81\cdot0.62 \\ F=255.45\text{ N} \end{gathered}[/tex]B.
First let's calculate the horizontal component of the weight:
[tex]\begin{gathered} F_x=m\cdot g\cdot\sin (35\degree) \\ F_x=42\cdot9.81\cdot0.5736 \\ F_x=236.33\text{ N} \end{gathered}[/tex]Now, let's calculate the friction force:
[tex]\begin{gathered} N=m\cdot g\cdot\cos (35\degree) \\ F=N\cdot\mu \\ F=m\cdot g\cdot\cos (35\degree)\cdot0.51 \\ F=42\cdot9.81\cdot0.819\cdot0.51 \\ F=172.1\text{ N} \end{gathered}[/tex]Since the horizontal compontent of the weight is greater than the friction force, she will slip off the roof.