Reattempt this question Question with last attempt is displa

Reattempt this question Question with last attempt is displayed for your review only As a fan turns counterelockwise, a bug sts 9.9 inches from the center of rotation on one of its blades. The bug is at the 3 o\'elock position on the fan when it begins to turn. If the fan makes less than one full rotation, determine the distance the bug has traveled along its arc from the 3 o\'clock position when its final position is. a... 4 1 inches to the right of the vertical diameter of the fan for the second time. 26.8744 b..5.7 inches to the left of the vertical diameter of the fan for the first time. e.... 6.4 inches to the left of the vertical diameter of the fan for the second time. t inches Preview Post this question to forum

Solution

distance from vertical diameter =x =rcos,distance from horizontal diameter =y =rsin

for 1 rotation 0 <2

given bug sits 9.8inches from center of rotation. so r =9.9 inches

=>x=9.9cos

(a)

right of vertical diameter for the second time=> bug is in 4^th quadrant

9.9cos = 4.1

=> =2 -cos^-1(4.1_/9.9)

distance bug travelled =r

distance bug travelled =9.9*(2 -cos^-1(4.1_/9.9)) inches exactly

distance bug travelled =50.88 inches approximately

(b)

left of vertical diameter for the first time=> bug is in 2^nd quadrant

9.9cos = -5.7

=> = -cos^-1(5.7_/9.9)

distance bug travelled =9.9*( -cos^-1(5.7_/9.9)) inches exactly

distance bug travelled =21.625 inches approximately

(c)

left of vertical diameter for the second time=> bug is in 3^rd quadrant

9.9cos = -6.4

=> = +cos^-1(6.4_/9.9)

distance bug travelled =9.9*( +cos^-1(6.4_/9.9)) inches exactly

distance bug travelled =39.694 inches approximately

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