A person of mass \(M\) slowly climbs a uniform ladder of length \(L\) and negligible mass that rests against a frictionless vertical wall and on a rough horizontal floor with coefficient of static friction \(\mu_s\). The ladder makes an angle \(\theta\) with the horizontal floor. If the ladder is repositioned so that the angle \(\theta\) is increased, how does the maximum distance along the ladder the person can climb before the ladder slips change, and what is the correct justification?