A ladder of length L=12 m and mass m=45kg leans against a slick wall (there is not friction among ladder and wall). The ladder's upper end is h=9.3 m above the floor. The coefficient of static friction among the ladder and the floor is μ=0.55. The ladder's center of mass is xcom=L/3 from the lower end, along the length of the ladder. A fire fighter of mass M=72kg climbs up the ladder.
What is the maximum distance (from the bottom of the ladder) that the fire fighter can climb up the ladder without causing the ladder to slipping?