A revolving searchlight, which is 100 m from the nearest point on a straight highway, casts a horizontal beam along a highway (see figure). The beam leaves the spotlight at an angle of π/16 rad and revolves at a rate of π/6 rad/s. Let w be the width of the beam as it sweeps along the highway and θ be the angle that the center of the beam makes with the perpendicular to the highway. What is the rate of change of w when θ = π/3? Neglect the height of the searchlight.

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O is the angle between the center of the beam and the line perpendicular to the highway. 100 m rad 16