Calculating Static Equilibrium for Ladder Climb

[PhysicsDud]

I'm not sure how to go about doing this question. Any help would be great.

A window cleaner of mass 95 kg places a 22-kg ladder against a frictionless
wall, at an angle 65° with the horizontal. The ladder is 10 m long and rests on a
wet floor with a coefficient of static friction equal to 0.40. What is the maximum
length that the window cleaner can climb before the ladder slips?

Thanks!

 

[Hootenanny]

Try taking moments about a point.

 

[vaishakh]

Draw a free body diagram and then find what force is enough for the ladder to slip. Here torqueplays the role. You take a general point on the ladderabove its centre. Find normal reaction, friction, torque, etc. And then equate them with the distance from centreas variable.

 

[vaishakh]

Sorry here centre of axis is not the centre of ladder, it is the poit at which it touches the surface..

 

[PhysicsDud]

Thanks

Thanks so much for the help!