Lance Armstrong's Power

The instantaneous power generated by a force that does work is the rate P = dW/dt at which it does work. The SI unit of power is the Watt, equal to 1 Joule per second. The average power is the work done by the force, divided by the time over which it was applied.  If the work done by a force F through a small displacement dx is dW = F . dx, then the instantaneous power is P = F . v.

At his training peak, Lance Armstrong was capable of generating 350 Watts with his aerobic metabolism, meaning that he could sustain this level of power output for extended periods of time.

(A) If we make the assumption that the rolling friction forces on the bicycle and air friction forces are negligible while climbing, how long would it take Lance Armstrong to climb a mountain in the Alps (Alpe d'Huez) with an elevation change of 1,000 m? Assume Lance has a mass of 66 kg and that his climbing bicycle has a mass of 7.5 kg.

(B) (Bonus question; your group will get an extra whiteboard point for today if you can show me by next class a solution that gives the right answer to the following:) There is a friction force on a rolling object (due to deformation of the object and the surface on which it rolls) called rolling friction. To a good approximation this is a constant force; for a good road bike this is 3.5 N. The air friction force on a bicyclist is proportional to the square of the square of the riders velocity, and has the value (0.26 kg/m ) v2, where v is in m/s. Using Armstrong's sustained power output, with what speed (in miles per hour) could he ride on level ground?