Estimate the power output of an elite cyclist pedaling a bicycle on a flat road at 14 m/s. Assume all energy is lost to air resistance, the cross-sectional area of the cyclist and the bicycle is 0.4 m², and the drag coefficient is 0.75. Now estimate the power output of the same elite cyclist pedaling a bicycle up a hill with slope 8% at 5 m/s. Compute the air resistance assuming the drag coefficient times cross-sectional area is c_dA = 0.45 m² (rider is in a less aerodynamic position). Compute the ratio of the power output to potential energy gain. Assume that the mass of the rider plus bicycle is 90 kg.