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 undergoes the following displacement.

A small boat is crossing a lake on a windy day. During some interval of time, the boat undergoes the following displacement. = (3.13 m)i+(2.83 mi Ar= 3.13 ml, + 2.83 m During the same interval of time, the wind exerts the following constant force on the boat. F259 Ni- (131 Nj F= 259 Ni-1131 N )j What is the total work done on the boat by the wind over this period of time? Number What is the angle between the direction of the wind force and the direction of the boat's motion during this time interval? Number

Explanation / Answer

a) work done = F.delta r = (259 i^ - 131 j^).(3.13 i^ + 2.83 j^) = 810.67 - 370.73 = 439.94 J

b) IFI = 290.24, Idelta rI = 4.22

Angle = cos-1[(F.delta r)/IFI*Idelta rI] = cos^-1[439.94/(290.24*4.22)] = 68.95 degree

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