The figure below shows the horizontal forces acting on a sailboat moving north a

Question

The figure below shows the horizontal forces acting on a sailboat moving north at constant velocity, seen from a point straight above its mast. At the particular speed of the sailboat, the water exerts a F = 330 - N drag force on its hull and ? = 33.0 degree . For each of the situations (a) and (b) described below, write two component equations representing Newton's second law. Then solve the equations for P (the force exerted by the wind on the sail) and for n (the force exerted by the water on the keel). Choose the x direction as east and the y direction as north. Now choose the x direction as ? = 33.0 degree north of east and the y direction as ? = 33.0 degree west of north. Compare your solutions to part (a) and (b). Do the results agree?

Explanation / Answer

a) Pcos(30) - n = 0
Psin(30) - D = 0, so P = D/sin(30) = 660 N
n = Pcos(30) = 572 N
b) P - ncos(30) - Dsin(30) = 0
nsin(30) - Dcos(30) = 0, so n = Dcos(30)/sin(30) = 572 N
P = ncos(30) + Dsin(30) = 660 N
c) yes

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