An eaeroplane is to go along straight line from A to B, and 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 the round trip is:

Options

A. `(2l)/(sqrt(V^(2)-nu^(2)))`
B. `(2vl)/(V^(2)-nu^(2))`
C. `(2vl)/(V^(2)-nu^(2))`
D. `(2l)/(sqrt(V^(2)+nu^(2)))`

Answer

A

Explanation

For no drift
`V sin theta =upsilon`
`sin theta =(upsilon)/V`
`:. t=t_(AB)+t_(BA)`
`t=(2l)/(V cos theta)`
=`(2l)/(Vsqrt(1-(upsilon^(2))/(V^(2))))`
`t=(2l)/(sqrt(V^(2)-upsilon^(2)))`