A plank AE, of length 6m and weight 100N, rests in a horizontal position on supports at B and D, where AB = 1m and DE =1.5m. A child of weight 145N stands at C, the mid-point of AE. The child is modelled as a particle and the plank as a uniform rod. The child and the plank are in equilibrium. Calculate the magnitude of the force exerted by the support on the plank at B and D.
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