A 5 m uniform ladder leans against a frictionless wall. The coefficient of static friction between the ladder and the floor is unknown. The base of the ladder is 3 m from the wall. If the ladder weighs 200 N, and a 800 N person is 4 m up the ladder (1 m from the top), what is the minimum coefficient of friction necessary between the ladder and the ground to keep the ladder from slipping? Show all work.