Math

Mary is riding a merry-go-round, whose radius is 25 feet and which is turning 36 degrees per second. Seeing a friend in the crowd, she steps off the the outer edge of the merry-go-round and suddenly finds it necessary to run? At how many miles per hour does she have to run?

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  1. since 1 revolution is 360 degrees,

    (25 * 2π ft/rev) * (2π/10 rev/s) * 3600s/hr * 1mi/5280 ft = 10.71 mi/hr

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  2. At the moment she steps off, her linear velocity equals the rate the arc length is increasing.

    circumference = 2π(25) = 50π ft
    36° = 36/360 = 1/10 of a rotation

    so the linear velocity of any point is 5π ft/second

    5π ft/1 second
    = (5π/5280) / (1/3600) miles/hour
    = (5π/(5280)(3600) mph
    = appr 10.7 mph

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