Answer to Question #126857 in Physics for Asif Sultan

Question #126857
http://prntscr.com/tkdo6a
1
Expert's answer
2020-07-22T10:35:12-0400

The displacement of the body is the line ABAB. Using the cosine law, from the triangle AOB\triangle AOB, we can find:


AB2=AO2+BO22ABBOcos120°=2R22R2cos120°AB^2 = AO^2 + BO^2 - 2AB\cdot BO\cos120\degree = 2R^2 - 2R^2\cos120\degree

using the trig identity:


cos(180°α)=cosα\cos(180\degree-\alpha) = -\cos\alpha

get:


AB2=2R2+2R2cos60°=2R2+2R212=3R2AB=3R2=R3AB^2 = 2R^2 + 2R^2\cos60\degree = 2R^2 + 2R^2\cdot \dfrac12 = 3R^2\\ AB = \sqrt{3R^2} = R\sqrt3

Answer. C-R3R\sqrt3.


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