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calc related rates

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A street light is at the top of a 18 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 45 ft from the base of the pole?

  • calc related rates - ,

    Draw a triangle.
    If the woman is x feet from the pole, and her shadow extends an additional y feet,

    18/(x+y) = 6/y
    18y = 6(x+y)
    18x = 6x + 6y
    12x = 6y
    2x = y

    2 dx/dt = dy/dt
    2(6) = dy/dt

    Now, the distance of the shadow tip from the pole is x+y, so its speed is dx/dt + dy/dt = 6+12 = 18 ft/sec, regardless of the distance.

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