Searchlight problem—narrow beam A searchlight is 100 in 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 ? /6 rad/s, find the rate at which the beam sweeps along the highway as a func ? tion of ??. For what? alue of ?? is this rate minimized?

Solution 42E Step 1: Given data S is the searchlight,P is the person and triangle QPS is the right angled triangle The searchlight rotates when the person is 100 meters from the searchlight Angular velocity of the searchlight, dt = 6ad/sec Step 2: From the given data we can draw the following figure