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20 September, 15:57

The worlds fastest humans can reach speeds of about 11 m/s in order to increase his gravitational potential energy by an amount equal to his Kinetic energy at full speed how high with the sprinter need to climb

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  1. 20 September, 16:04
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    What a delightful little problem!

    - - When he is running on level ground, his kinetic energy is

    KE = (1/2) x (mass) x (speed) ².

    - - When he climbs up from the ground, his potential energy is

    PE = (mass) x (gravity) x (height above the ground).

    We're looking for the height that makes these quantities of energy equal,

    figuring that when he runs, his speed is 11 m/s.

    The first time I looked at this, I thought we would need to know the runner's

    mass. But it turns out that we don't.

    PE = KE

    (mass) x (gravity) x (height) = (1/2) (mass) (11 m/s) ²

    Divide each side by (mass):

    (gravity) x (Height) = (1/2) (11 m/s) ²

    Divide each side by gravity:

    Height = (1/2) (121 m²/s²) / (9.8 m/s²)

    = 6.173 meters

    (about 20.3 feet!)
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