An aeroplane flies along a straight line from A to B with a speed v₀ and back again with the same speed v₀. A steady wind v is blowing. If AB = 1 then
a) total time for the trips is $\frac{2 v_{0} l}{v_{0}^{2} - v^{2}}$ if wind blows along the line AB
b) total time for the trip is $\frac{2 l}{\sqrt{v_{0}^{2} - v^{2}}}$ , if wind blows perpendicular to the line AB
c) total time for the trip decrease because of the presence of wind
d) total time for the trip increase because of the presence of wind

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a, b, c are correct

only a, d are correct

a, b, d are correct

only b, d are correct

answer is A.

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Detailed Solution

When wind is along AB
$\begin{array}{l} t_{1} = \frac{AB}{v_{0} - v} = \frac{l}{v_{0} - v} \\ t_{2} = \frac{AB}{v_{0} + v} = \frac{1}{v_{0} + v} \\ t = t_{1} + t_{2} = \frac{2 v_{0}}{v_{0}^{2} - v^{2}} \end{array}$
When the wind is perpendicular to AB relative velocity along AB and BA are equal in magnitude
$\begin{array}{l} v_{rel} = \sqrt{v_{0}^{2} - v^{2}} \\ t = t_{1} + t_{2} = \frac{1}{\sqrt{v_{0}^{2} - v^{2}}} + \frac{1}{\sqrt{v_{0}^{2} - v^{2}}} \\ t = \frac{2 l}{\sqrt{v_{0}^{2} - v^{2}}} \end{array}$
Total time for the trip increases, because of the presence of wind