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A bicyclist of mass 75 kg (including the bicycle) can coast down a 4.0^{} hill at a steady speed of 12 km/h. Pumping hard, the cyclist can descend the hill at a speed of 32 km/h.

Using the same power, at what speed can the cyclist climb the same hill? Assume the force of friction is proportional to the square of the speed v; that is, F_{fr} = bv^{2}, where b is a constant.

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