Question

An elite Tour de France cyclist can maintain an output power of 450 W during a sustained climb. At this output power, how long would it take an 88 kg cyclist (including the mass of his bike) to climb the famed 1100-m-high Alpe d'Huez mountain stage?

Answer 1

T = 35' 08"

Step-by-step explanation:

• By definition, the power is the rate of change of energy, with respect to time:

`P = (\Delta E)/(\Delta t) (1)`

• ΔE, in this case, must be equal to the change in the gravitational potential energy during the climb (neglecting friction), as follows:

`\Delta E = m*g*h = 88 kg*9.8m/s2*1100 m = 948640 J (2)`

• From (1) and (2), being P= 450 W, we can solve for Δt, as follows:

`\Delta t = (\Delta E)/(P) = (948640J)/(450W) = 2108 sec. (3)`

• Converting seconds to minutes, we get:
• Δt = 35' 08"