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Question

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(a) Choose the x direction as east and the y direction as north.
             

(b) Now choose the x direction as ? = 31.5° north of east and the y direction as ? = 31.5° west of north.

n = (.................................) N

P = (.................................) N

n =      N P =               N 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 Farrowbold = 432-N drag force on its hull and ? = 31.5 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).

Explanation / Answer

I think the ? in the question is the angle, and will base my answer on it.

Given that the boat moves with constant velocity, so , force acting on it cancels out.

Resultant force = 0

a) F = 432N = Psin(angle) = Psin(31.5)

So, P = 826.8 N

n = Pcos(angle) = 826.8cos(31.5)

n = 704.96 N

b) Fcos(angle) = 432cos(31.5) = 368.34 N = nsin(31.5)

n = 704.96 N

P = Fsin(angle) + ncos(angle) = 432sin(31.5) + 704.96cos(31.5)

P = 826.8 N

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