Question: A light is to be placed atop a pole of height feet to illuminate a busy traffic circle, which has a radius of 40 ft.

A light is to be placed atop a pole of height feet to illuminate a busy traffic circle, which has a radius of 40 ft. The intensity of illumination at any point P on the circle is directly proportional to the cosine of the angle (see the figure) and inversely proportional to the square of the distance from the source.
(a) How tall should the light pole be to maximize l?
(b) Suppose that the light pole is feet tall and that a woman is walking away from the base of the pole at the rate of 4 ft/s. 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 traffic circle?

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