A searchlight is 100 m from the nearest point on a straight highway (see figure). As it

Question:

A searchlight is 100 m from the nearest point on a straight highway (see figure). As it rotates, the searchlight casts a horizontal beam that intersects the highway in a point. If the light revolves at a rate of π/6 rad/s, find the rate at which the beam sweeps along the highway as a function of θ. For what value of θ is this rate maximized?

Overhead view 100 m Highway