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An aeroplane flies along a straight path...

An aeroplane flies along a straight path `A and B` and returns back again. The distance between `A and B` is `l` and the aeroplane maintains the constant speed `v` w.r.t. wind.
There is a steady wind with a speed `u` at an angle `theta` with line `A B`. Determine the expression for the total time of the trip.
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Text Solution

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A to B
Velocity of plane along` AB =v cos alpha-ucos theta`,
and for no - drift from line .
AB: `v sin alpha = usintheta rArr sin alpha (u sin theta)/v`
time taken from A to B `t_(AB)=l/(v cosalpha - u cos theta)`

B to A
velocity of plane along BA=`v cos alpha +u cos theta`
and for no drift from line AB: `v sin alpha = usin theta rArr sin alpha (usin theta)/v`
total time taken `t_(AB)+t_(BA)=(2vl cos alpha)/(v^(2) cos^(2) alpha-u^(2) cos^(2) theta)= 2vlsqrt(1-(u^(2)sin^(2)theta)/v^(2))/(v^(2)-u^(2))`
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