In the following diagram is a ladder of length 10 m and mass 34 kg. End of the ladder is resting against a smooth vertical wall, while end rests on rough horizontal ground so that the ladder makes an angle of 60° with the ground as shown below:
A housepainter with a mass of 75 kg has decided to climb up the ladder without taking any additional precautions to prevent the bottom of the ladder from slipping. The ladder may be modelled as a uniform rod lying in a vertical plane perpendicular to the wall, and the housepainter may be modelled as a particle. The coefficient of friction between the ground and the ladder is 0.4.
Luckily, the housepainter’s partner convinces him not to climb up the ladder without providing some additional support at the bottom to prevent slipping. If the housepainter had continued with his original plan, however, how far above the ground would he have been when the ladder began to slip?