ExaMple 5 A man wakes along a straight path at a speed of 5 fu/s. A searchight is located on the ground 4 it from the gath and is kept locused on the man. At what rate is the seacchlight rotating ahen the man is 3 ft from the point on the path dicsest to the searchlight? souvtion We draw the figare to the left and let x be the ostance frem the man to the ppint on the path cosest to the acarchight. We let be the asyle between the beam of the soarthight and the perpendicular to the path. We are civen that dx/dt =5ft/s and are asked to find duf/ot nhen x=3. The equation that relates x and 9 can be writen Arem the figure: x=tan()x=tan() D.Merentiating each vise with respect to t, we pet dtdx= dt90= (s) When x=3, the length of ere beam is 5, se custo =54 and atitit=(1)2= The seprobisht is potating at inte of ExaMple 5 A man wakes along a straight path at a speed of 5 fu/s. A searchight is located on the ground 4 it from the gath and is kept locused on the man. At what rate is the seacchlight rotating ahen the man is 3 ft from the point on the path dicsest to the searchlight? souvtion We draw the figare to the left and let x be the ostance frem the man to the ppint on the path cosest to the acarchight. We let be the asyle between the beam of the soarthight and the perpendicular to the path. We are civen that dx/dt =5ft/s and are asked to find duf/ot nhen x=3. The equation that relates x and 9 can be writen Arem the figure: x=tan()x=tan() D.Merentiating each vise with respect to t, we pet dtdx= dt90= (s) When x=3, the length of ere beam is 5, se custo =54 and atitit=(1)2= The seprobisht is potating at inte of