A) 2v cos \[{{40}^{{}^\circ }}\]
B) 2v sm \[{{40}^{{}^\circ }}\]
C) 2v cos \[{{20}^{{}^\circ }}\]
D) 2v sin \[{{20}^{{}^\circ }}\]
Correct Answer: B
Solution :
Apply principle of vector subtraction \[\Delta v=\sqrt{{{v}^{2}}+{{v}^{2}}+2vv\,\cos \,{{40}^{{}^\circ }}}\] \[=\sqrt{2{{v}^{2}}\,(1-\cos \,{{40}^{{}^\circ }})}\] \[=\sqrt{2{{v}^{2}}\,[2{{\sin }^{2}}\,{{20}^{{}^\circ }}]}\] \[=2v\,\sin \,{{20}^{{}^\circ }}\]
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