Kinematics Question 526

Question: An aeroplane is to go along straight line from $ A $ to $ B $ , am back again. The relative speed with respect to wind it’s $ V $ The wind blows perpendicular to line AB with speed v The distance between $ A $ and $ B $ it’s $ l $ . The total time for round trip it’s

Options:

A) $ \frac{2\ell }{\sqrt{V^{2}-v^{2}}} $

B) $ \frac{2v\ell }{V^{2}-v^{2}} $

C) $ \frac{2V\ell }{V^{2}-v^{2}} $

D) $ \frac{2\ell }{\sqrt{V^{2}+v^{2}}} $

Show Answer

Answer:

Correct Answer: A

Solution:

[a] For no drift: $ V\sin \theta =v $

$ \sin \theta =\frac{v}{V} $

$ \therefore t=t _{AB}+t _{BA} $

$ t=\frac{2\ell }{V\cos \theta }=\frac{2\ell }{V\sqrt{1-\frac{v^{2}}{V^{2}}}}\Rightarrow t=\frac{2\ell }{\sqrt{V^{2}-v^{2}}} $



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