A uniform stationary ladder of length L = 4.5 m and mass M = 14 kg leans against a smooth vertical wall, while its bottom legs rest on a rough horizontal floor. The coefficient of static friction between floor and ladder is μ = 0.36. The ladder makes an angle θ = 59^o with respect to the floor. A painter of weight 8M stands on the ladder a distance d from its base.

Randomized Variables

L = 4.5 m

M = 14 kg

μ = 0.36

θ = 59^o

Magnitude = 1236.

What is the largest distance up the ladder d_max, in meters, that the painter can stand without the ladder slipping?