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Calculate the minimum average power output necessary for a 87.4 kg person to run up a 12.0 m long hillside, which is inclined at 25.0° above the horizontal, in 3.00 s. You can neglect the person's kinetic energy. Express your answer in horsepower.

Respuesta :

Answer:

P = 1447.51 Watts

Explanation:

Given that,

Mass of the person, m = 87.4 kg

Length of the hillside, l = 12 m

Inclination above horizontal, [tex]\theta=25^{\circ}[/tex]

Time, t = 3 s

Let h is the height of the hillside, it can be calculated using trigonometry.

[tex]h=l\ sin(25)[/tex]

[tex]h=12\times \ sin(25)[/tex]

h = 5.07 m

Let P is the minimum average power output. It is equal to the energy per unit time. Its formula is given by :

[tex]P=\dfrac{E}{t}[/tex]

[tex]P=\dfrac{mgh}{t}[/tex]

[tex]P=\dfrac{87.4\times 9.8\times 5.07}{3}[/tex]

P = 1447.51 Watts

So, the minimum average power output of the person is 1447.51 Watts. Hence, this is the required solution.

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