A light is to be placed atop a pole of height h feet to

Chapter , Problem 85

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A light is to be placed atop a pole of height h feet to illuminate a busy trafc circle, which has a radius of 40 ft. The intensity of illumination I at any point P on the circle is directly proportional to the cosine of the angle (see the gure) and inversely proportional to the square of the distance d from the source. (a) How tall should the light pole be to maximize I? (b) Suppose that the light pole is h feet tall and that a woman is walking away from the base of the pole at the rate of 4 ftys. At what rate is the intensity of the light at the point on her back 4 ft above the ground decreasing when she reaches the outer edge of the trafc circle?