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15 January, 07:21

A new record for running the stairs of the Empire State Building were set on February 4, 2003. The 86 flights, with a total of 1576 steps, was run in 9 minutes and 33 seconds. If the height gain of each step was 0.20 m, and the mass of the runner was 70.0 kg, what was his average power output during the climb? Give your answer in both watts and horsepower.

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  1. 15 January, 07:48
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    Power = 377.35 W or Power = 0.5065 hp

    Explanation:

    Given:

    Number of steps, n = 1576

    height of each step, h = 0.20 m

    Total height achieved, H = nh = 1576 * 0.20 = 315.2 m

    Mass of the runner, M = 70.0 kg

    Total time taken, t = 9 minutes 33 seconds = (9 * 60) + 33 = 573 seconds

    Now, the potential energy gained by the runner,

    E = MgH

    where, g is the acceleration due to the gravity

    on substituting the values in the above formula, we get

    E = 70 * 9.8 * 315.2

    or

    E = 216227.2 J

    also,

    Energy = Power * time

    therefore,

    Power = Energy/time

    or

    Power = 216227.2 J / 573

    or

    Power = 377.35 W

    Now,

    745 watt = 1 hp

    or

    1 watt = 1/745 hp

    thus,

    Power = 377.35 W = 337.35 * (1/745) hp

    or

    Power = 0.5065 hp
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