As a sailboat sails 58 m due north, a breeze exerts a constant force f1 on the boat's sails. this force is directed at an angle west of due north. a force f2 of the same magnitude directed due north would do the same amount of work on the sailboat over a distance of just 44 m. what is the angle between the direction of f1 and due north?

Question

Dayanara Torres

Physics

17 July, 11:23

As a sailboat sails 58 m due north, a breeze exerts a constant force f1 on the boat's sails. this force is directed at an angle west of due north. a force f2 of the same magnitude directed due north would do the same amount of work on the sailboat over a distance of just 44 m. what is the angle between the direction of f1 and due north?

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Dorian Vaughan · Answer 1

Let x = angle between due north and west of due north, exerted by f1.

Note that work = force * distance.

The component of force f1 that acts due north is f1*cos (x). It acts over 58 m.

The force f2 (equal in magnitude to f1) acts due north over 44 m.

Because the work produced is the same, therefore

f1*cos (x) * 58 = f1*44

58cos (x) = 44

cos (x) = 44/58 = 0.7586

x = arcos (0.7586) = 40.66°

Answer: 40.7° (nearest tenth)