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 = 153-N drag force on its hull and theta = 50.0 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). (a) Choose the x direction as east and the y direction as north. Now choose the x direction as theta = 50.0 degree north of east and the y direction as theta = 50.0 degree west of north. Compare your solutions to part (a) and (b). Do the results agree?

Explanation / Answer

a) x direction equation P cos? -n =0 y direction P sin ? - F = 0 so P sin ?/ P cos ? = F/n tan ? = F/n n = F/ tan? = 153/tan(50)= 128.4 so P sin(50)=153 P =153/sin(50)=199.7 b) now x direction is 50 degrees so x direction equation P - n cos 50 - F cos 40 y direction n sin 50 - F sin 40 = 0 n = 153 sin 40/ sin 50 = 128 .4 and plug into x direction P = 128.4 cos 50 + 153 cos 40 = 199.7

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