Question

A winch at the top of a 12-meter building pulls a pipe of the same length to a vertical position, as shown in the figure. The winch pulls in rope at a rate of -0.3 meter per second (ds/dt = -0.3 m/sec). Find the rate of vertical change and the rate of horizontal change at the end of the pipe when y = 4. (Round your answers to three decimal places.) (x, y) 12 m 6 horizontal m/sec vertical m/sec Need Help? Read It Talk to a Tutor

Answer 1

C 12-7 ç B X Y A using Pythagorean in in AABE **+y2 = 122 at y=4 x²+42=122 12 x2+16=144 X2=144-16=128 X=128=812 In ACBE x2+(12-y)2 = 32 to use X=812, Y-4 (813)2+(12-4)2 = $2 $2 = 128+64 = 192 → S = V192 = 813 - x2+y2 = 122 -differentiate with respect to t dy 2x dx dy +2y =0 27 2x AN dx dx dt dt 7P dt dy at x de la Now, -dy 37 = ds dt dt =S ds at *2+(12-y)2 =$2 2x dx + 2 +2(12-y)( to + (12-Y) ( cente (x+(12-y))= det (x+ 12x -x)=s (123) = dx dt s ds dt ds dt dx/ 12X at 3 ds dt dx sy ds at 12x dt ds S=813 dt -0.3 uçe X=812, =4 so, - dx at (813)(4) 121812) (-0.3 -0.122 m/s dy at x. dx y at BvE (813)4)(-0.3) 121812) - - 4 dy at = 0.346 m/s