Physics Two Dimensional Motion Question 73
Question: 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
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}}} $
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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}}} $
BETA
