against a vertical wall. The coefficient is as indicated. In addition to its own weight a man stands on the top with a weight of $90N.$

rigure Q$1$

Calculate:

$($a$)$ The horizontal force $P$ to be applied to the ladder at the floor level to prevent slipping.

$($b$)$ If the force $P$ is applied to the ladder, what is the minimum angle of the ladder with the horizontal so that no slipping occurs?