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17 days ago

14

Calculate the minimum average power output necessary for a person to run up a 12.0 m long hillside, which is inclined at 25.0° a

bove the horizontal, in 3.00 s. You can neglect the person's kinetic energy. Express your answer in horsepower

1 answer:

Ostrovityanka [2.2K]17 days ago

3 0

Answer:

Power output, P = 924.15 watts

Explanation:

We have the following parameters:

Length of the ramp, l = 12 m

Weight of the individual, m = 55.8 kg

Incline angle with respect to the horizontal, $\theta=25^{\circ}$

Elapsed time, t = 3 s

Let h represent the vertical height of the hill:

$h=l\ sin\theta$

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

h = 5.07 m

Power P required for a person to ascend the hill can be expressed as:

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

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

$P=\dfrac{55.8\times 9.8\times 5.07}{3}$

P = 924.15 watts

This indicates that a minimum average power output of 924.15 watts is essential for an individual to ascend this elevation. Thus, this is the answer sought.

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The horizontal component is described as follows:

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Rearranging the equation above to isolate $\mu$ leads to:

$\mu \ = \ \frac{F_X}{mg - F_Y}$

Substituting in the following values:

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