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March 27, 2017

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A street light is mounted at the top of a 19-ft-tall pole. A man 5.5 feet tall walks away from the pole with a speed of 14 ft/s along a straight path. How fast is the tip of his shadow moving when he is 100 feet from the pole?

  • math - ,

    If the man is x feet from the pole, and his shadow has length s, then by similar triangles,

    (x+s)/19 = s/5.5
    19s = 5.5(x+s)
    13.5s = 5.5x
    s = .407x
    The tip of the shadow is at distance x+s = 1.407x

    so, it is moving with speed

    d(x+s)/dt = 1.407 dx/dt
    = 1.407*14 = 19.7 ft/s

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