EXAMPLES A man walks along a straight path at a speed of 25 m/s. A searchlight is located on the ground 6 m from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is a m from the point on the path closest to the searchlight? SOLUTION We draw the figure to the left and let x be the distance from the man to the point on the path chosest to the searchlight. We leto be the angle between the beam of the searchlight and the perpendicular to the path We are given that da/dt - 2.5 m/s and are asked to find da/dt win = . The equation that relates X and can be written from the figure tan() tande). Differentiating each side with respect to t, we get 00 Video Example 45 When xw, the length of the beam is 10, so con) - and The searchlight is rotating at a rate of rad/ Activate Windows Gotong divate Wed