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An elite Tour de France cyclist can maintain an output power of 440W during a sustained climb.At this output power, how long would it take an 81kg cyclist (including the mass of his bike) to climb the famed 1100-m-high Alpe d'Huez mountain stage? Neglect any friction.

Respuesta :

Potential energy is given by :

[tex]P.E = mgh_f - mgh_i\\\\P.E = 81\times 10( 1100 - 0 )\ J\\\\P.E = 891000\ J[/tex]

It is also given that power supplied is 440 W.

Let, time taken to reach the Alpe d'Huez mountain stage is t.

So,

[tex]t = \dfrac{891000}{440}\ s\\\\t = 2025 \ s \ or\ (\ 33 \ min \ 45\ ) \ sec[/tex]

Hence, this is the required solution.

Lanuel

The amount of time it would take the cyclist to climb Alpe d'Huez mountain stage is 1,984.5 seconds.

Given the following data:

  • Power = 440 Watts
  • Mass = 81 Kg
  • Height = 1100 meter

Scientific data:

  • Acceleration due to gravity = 9.8 [tex]m/s^2[/tex]

To determine the amount of time it would take the cyclist to climb Alpe d'Huez mountain stage:

First of all, we would calculate the potential energy possessed by the cyclist and his bike:

[tex]P.E = mgh\\\\P.E = 81 \times 9.8 \times 1100[/tex]

Potential energy = 873,180 Joules

Mathematically, power is given by the formula:

[tex]Power = \frac{Energy}{time}[/tex]

Making time the subject of formula, we have:

[tex]Time = \frac{Energy}{Power}[/tex]

Substituting the given parameters into the formula, we have;

[tex]Time = \frac{873180}{440}[/tex]

Time = 1,984.5 seconds.

Read more: https://brainly.com/question/12193740

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