A uniform ladder AB, of mass m kilograms and length 2a metres, has one end A on rough horizontal ground. The other end B rests against a smooth vertical wall. The ladder makes an angle a with the vertical, where tan a = .3A42child of mass 2m kilograms stands on the ladder at C where AC =a, as shown in the diagram. The ladder and the child are in equilibrium. Model the ladder as a rod and the child as a particle. a) Draw a diagram showing all the forces actingon the ladder b) Calculate the least possible value of the coefficient of friction between the ladder and the ground.

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