A sailboat can be propelled into the wind by a maneuver called beating to windwa

Question

A sailboat can be propelled into the wind by a maneuver called beating to windward. Beating requires the sailboat to travel in a zigzag pattern at an angle to the wind that is greater than the no-go zone, which is shaded red in When a sailboat is just outside the no-go zone (boats B in the figure) the wind exerts a force F on the sail that hasa component in the direction of motion v Similar comments apply to boats C. The work done by the wind on the sail is W = Fdcost, and because u = d/ t, the propulsion power PW/t delivered to the sailboat is Fucot, where is the angle between the sail force and the direction of motion. Winddirection Part A Assuming that F and v have the same magnitudes for each sailboat, will the propulsion power delivered to sailboats B be greater than, less than, or the same as the propulsion power delivered to sailboats C? O Greater than O Less than Equal to Request Answer Part B If F = 890 N and U-15 m/s, what propulsion power is delivered to sailboats B, for which = 74° ? Express your answer to two significant figures and include appropriate units. alue Units . Part C What propulsion power is delivered to sailboats C, for which = 53° ? Express your answer to two significant figures and include appropriate units. alue Units

Explanation / Answer

Since the values of F and v are same for both B and C boats and propulsion power is given by Fvcos(theta), cos(theta) becomes the decisive factor.

In the case of B, the theta value looks greater than that of C. But the cos of lesser value yields greater output.

Hence cos(theta) is greater for C.

So Propulsion power for B will be less than C

b)

Propulsion power = Fv cos(theta) ===> 3679.7587 watts

c)

Propulsion power = Fv cos(theta) ====> 8034.2305 watts

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