Video Example\" EXAMPLE 5 A man walks along a straight path at a speed of 2 ftls. A searchlight is located on the ground 8 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 6 ft from the point on the path closest to the searchlight? SOLUTION We draw the gure to the left and let x be the distance from the man to the point on the path closest to the searchlight. We let i? he the angle between the beam of the searchlight and the perpendicular to the path. We are given that dxfdt = 2 ftls and are asked to nd didt when x = 6. The equatiOn that relates x and 3 can be written from the figure: X = tani) x = .r tanw). Differentiating each side with respect to t. we get $3. = m 3 Your answer cannot be understood or graded. More Information % 50 d3 dt 1 E (:03 ( 2 )3 x Your answer cannot be understood or gra 1 = ECOS( 2 )9 x Your answer cannot be understood or grad