Question

13. A 18-ft ladder leaning against a wall begins to slide. How fast is the angle between the ladder and the wall changing at the instant of time when the bottom of the ladder is 9 ft from the wall and sliding away from the wall at the rate of 4 ft/sec? Round the answer to the nearest hundredth. I

Answer 1

Given 2. when x=9 =) x² + y 2 =18² =) 9² +4²=182 y= y = √243 =983 =) √ 18²92 12= 2 o y a Given da TE uft/sec Z Seco= dy dt = 18 who lo con Ko ? By Pythogorous theolm n²ty ² = 2 ² = 18² on both sides (a?+y2)=5 (182) Differentiating on 2 Seco El dt d JE = 0 da +2(8243 dy =0 dt :) and x + 2 y tu -) 219) :) 9 (4) + 8243 dy dt -O dt م ك 9 he dy dt = = V243 لا اک h - dy dt EN al Tano = co (Differentiating) sech o do x=9, da dt dy. do dt ( .y V 21 = dt y² Y = 913 dm = 4 dy -y dt

=> (8)* * ч (43) - (-) (9) (93) - 30 3kv3 + - Ч 3 do dt 3 — 243 98 +8o | 3 -) do dt — V/3 23 X4 и , Ч B (t4u 23 ху 2 7 да Ч 93 2 Ч da degree/sec о dt 9г