(1 point) As a fan turns counterclockwise, a bug sits 27 cm from the center of r
ID: 2906134 • Letter: #
Question
(1 point) As a fan turns counterclockwise, a bug sits 27 cm from the center of rotation on one of its blades. The bug is at the 3 o'clock position on the fan when it begins to turn (Click on the graph to get a larger version.) 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) 6 cm to the left of the vertical diameter of the fan for the first time. Cm b) 20 cm to the left of the vertical diameter of the fan for the second time Cm c) 15 cm to the right of the vertical diameter of the fan for the second time CmExplanation / Answer
a) 6cm to the left of vert, dia.
cos(theta) = 6/27 ;
theta = cos^-1(6/27) = 1.34 rad
distance along the arc= (2pir)/2pi)*1.34 = 36.18 cm
b) 20 cm to the left of dia for second time:
theta = cos^-1(20/27) = 0.736
distance along the arc= {(2pi*r)/2pi}*{2pi +0.736} = 189.51 cm
c) 15 cm to the right of the vertical dia. for second time :
theta = cos^1(15/27) = 0.9817
distance along the arc= {(2pi*r)/2pi}*(2pi +0.9817) = 196.15 cm
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