A ladder $$\(A B\)$$ has length $$\(6 \mathrm{~m}\)$$ and mass $$\(30 \mathrm{~kg}\)$$. The ladder rests in equilibrium at $$\(60^{\circ}\)$$ to the horizontal with the end $$\(A\)$$ on rough horizontal ground and the end $$\(B\)$$ against a smooth vertical wall, as shown in Figure 3. A man of mass $$\(70 \mathrm{~kg}\)$$ stands on the ladder at the point $$\(C\)$$, where $$\(A C=2 \mathrm{~m}\)$$, and the ladder remains in equilibrium. The ladder is modelled as a uniform rod in a vertical plane perpendicular to the wall. The man is modelled as a particle. (a) Find the magnitude of the force exerted on the ladder by the ground. (6) The man climbs further up the ladder. When he is at the point $$\(D\)$$ on the ladder, the ladder is about to slip. Given that the coefficient of friction between the ladder and the ground is 0.4 (b) find the distance $$\(A D\)$$. (4) (c) State how you have used the modelling assumption that the ladder is a rod. (1)

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