question_answer

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

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) \[\frac{2\ell }{\sqrt{{{V}^{2}}+{{v}^{2}}}}\]

Correct Answer: A

Solution :

[a] For no drift: \[V\sin \theta =v\] \[\sin \theta =\frac{v}{V}\] \[\therefore t={{t}_{AB}}+{{t}_{BA}}\] \[t=\frac{2\ell }{V\cos \theta }=\frac{2\ell }{V\sqrt{1-\frac{{{v}^{2}}}{{{V}^{2}}}}}\Rightarrow t=\frac{2\ell }{\sqrt{{{V}^{2}}-{{v}^{2}}}}\]