Question

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.

Answer 1

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, $\theta=25^{\circ}$

Time, t = 3 s

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

$h=l\ sin(25)$

$h=12\times \ sin(25)$

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 :

$P=\dfrac{E}{t}$

$P=\dfrac{mgh}{t}$

$P=\dfrac{87.4\times 9.8\times 5.07}{3}$

P = 1447.51 Watts

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