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A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 40 ft from the base of the pole?

  • calculus -

    L = pole to shadow tip
    x = pole to walker
    so (L-x) = walker to shadow tip
    L/16 = (L-x)/6 (similar triangles)
    6 L = 16 L - 16 x

    16 x = 10 L
    L = 1.6 x
    dL/dt = 1.6 dx/dt

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