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 rightarrow = 374-N drag force on its hull and ? = 46.5 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). Choose the x direction as east and the y direction as north. Now choose the x direction as ? = 46.5 degree north of east and the y direction as ? = 46.5 degree west of north. Compare your solutions to part (a) and (b). Do the results agree?

Explanation / Answer

the velocity of sailboat is constant hence net force acting on the body is zero a) for equilibrium in y direction P sin(theta) = F P* sin(46.5) = 374 P = 515.6 N for euilibrium in x direction n = P cos(theta) n = 515.6 cos(46.5) n = 354.9 N b) now considering x direction as 46.5 degree north of east i.e, direction of x is along the direction of P and the y direction perpendicular to it for equilibrium in x direction, n sin(theta) = F cos(theta) n sin(46.5) = 374 cos(46.5) n = 354.9 N for equilibrium in y direction, P = n cos(theta) + F sin(theta) P = 354.9*cos(46.5) + 374*sin(46.5) P = 515.6 N c) solutions in both part are same yes the results agree, the forces does not depend on the axis chosen, in each and every direction the forces should be balanced then only the body will be in equilibrium

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