A uniform ladder AB of length 5m and weight 300N rests with its lower end A on a rough horizontal floor and its upper end B against a smooth vertical wall. The coefficient of static friction between the ladder and the floor is 0.40.
(i) Draw the free-body diagram of the ladder, indicating all forces acting on it.
(ii) Establish an expression that relates the angle θ which the ladder makes with the floor to the given coefficient of friction when the ladder is on the point of slipping.
(iii) Determine the least value of θ for which the ladder remains in equilibrium, and compute the corresponding magnitudes of the normal reaction at the floor and the normal reaction at the wall.