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}}} $
