MapO Sapling Learning macmillan learning A small boat is crossing a lake on a wi

Question

MapO Sapling Learning macmillan learning A small boat is crossing a lake on a windy day. During some interval of time, the boat undergoes the following displacement. Ar= (3.19 m), + (2.75 m During the same interval of time, the wind exerts the following constant force on the boat F= (257 N)--(129 N)j What is the total work done on the boat by the wind over this period of time? Number 465.08 What is the angle between the direction of the wind force and the direction of the boat's motion during this time interval? Incorrect See lower panel for more information. Number 74.91

Explanation / Answer

total work done W = F. S

F = wind force

S = displacement

Work = ( (257 N)i - (129 N) j ) . ((3.19m)i + (2.75 m)j)

work = (257*3.19) - (129*2.75) J

work = 465.08 J

===================================

angle = cos^-1( F.S/ (lFl*lSl) )

magnitude of F = lFl = sqrt(257^2+129^2) = 287.6 N

magnitude of S = lSl = sqrt(3.19^2+2.75^2) = 4.21 m

angle = cos^-1((465.08/(287.6*4.21)) = 67.4

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