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A street light is at the top of a 15.000 ft. tall pole. A man 6.300 ft tall walks away from the pole with a speed of 6.000 feet/sec along a straight path. How fast is the tip of his shadow moving when he is 45.000 feet from the pole?

  • calculus -

    using similar triangles, we see that if the man is x from the pole, and his shadow is s long,

    (x+s)/15 = s/6.3
    6.3x + 6.3s = 15s
    6.3x = 8.7s
    So, if x is increasing and s is increasing, then the tip of the shadow is moving at speed dx/dt + ds/dt.

    Or, dx/dt (1 + 6.3/8.7)

    Note that it does not matter how far from the pole the man is.

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