A small boat is crossing a lake on a windy day. During some interval of time, th

Question

A small boat is crossing a lake on a windy day. During some interval of time, the boat u following displacement. Ar=(3.11 m) i +(2.79 m)/ During the same interval of time, the wind exerts the following constant force on the boat. F-(265 Ni-19 N What is the total work done on the boat by the wind over this period of time? Incorrect See lower panel for more information. Number 861.4 What is the angle between the direction of the wind force and the direction of theboas motion during this time interval? Number

Explanation / Answer

work done = F.r

= (265i - 119j).(3.11i + 2.79 j)

= 265*3.11 + (-119*2.79)

= 492.14 J

magnitude of F = sqrt(265^2 + 119^2) = 290.5 N

magnitude of r =sqrt(3.11^2 + 2.79^2) = 4.18 m

angle = cos^-1(492.14 / 290.5*4.18)

= 66.1o

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