Predict/Calculate Beating to Windward A sailboat can be propelled into the wind by a maneuver called beating to windwand. Beating requires the sailboat to travel in a zigzag pattern at an angle to the wind that is greater than the $n a-g o$ zone, which is shaded red in FIGURE $7-23$ . When a sailboat is just outside the no-gozone (boats B in the figure) the wind exerts a force $\overline{\mathbf{F}}$ on the

sail that has a component in the direction of motion $\overline{\mathbf{v}}$ . Similar comments apply to boats C. The work done by the wind on the sail is $W=F d \cos \theta,$ and because $v=d / t,$ the propulsion power $P=W / t$ delivered to the sailboat is $F v \cos \theta,$ where $\theta$ is the angle

between the sail force and the direction of motion. (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? Explain. (b) If $F=870 \mathrm{N}$ and $v=11 \mathrm{m} / \mathrm{s},$ what propulsion power is delivered to sailboats $B$ , for which $\theta=79$ ?

(c) What propulsion power is delivered to sailboats $C,$ for which $\theta=56^{\circ} ?$