69_Physics ProblemsTechnical Physics

69_Physics ProblemsTechnical Physics - 70 Vectors...

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70 Vectors Additional Problems P3.51 Let θ represent the angle between the directions of A and B . Since A and B have the same magnitudes, A , B , and RAB =+ form an isosceles triangle in which the angles are 180 ° , 2 , and 2 . The magnitude of R is then RA = F H G I K J 2 2 cos . [ Hint: apply the law of cosines to the isosceles triangle and use the fact that BA = . ] Again, A , – B , and DAB = form an isosceles triangle with apex angle . Applying the law of cosines and the identity 12 2 2 −= F H G I K J cos sin af gives the magnitude of D as DA = F H G I K J 2 2 sin . The problem requires that RD = 100 . Thus, 2 2 200 2 AA cos sin θθ F H G I K J = F H G I K J . This gives tan . 2 0010 F H G I K J = and 115 .. A B R /2 A D –B FIG. P3.51 P3.52 Let represent the angle between the directions of A and B . Since A and B have the same magnitudes, A , B , and
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