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. .

An aeroplane flies along a straight path A and B and returns back agai

1.	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. .
Answer» SOLUTION :SUPPOSE the plane is oriented at an angle `PROP` w.r.t. line `AB`, while the plane is moving from `A` to `B` : Velocity of plane ALONG `AB = v cos prop - u cos theta`, and for no - drift from line `AB` `v sin prop = u sin theta` `rArr sin prop = (u sin theta)/(v)` Time taken from `A` to `B ` : `t_(A B) = (l)/(v cos prop - u cos theta)` Suppose plane is oriented at an angle `prop` w.r.t. line `AB` while the plane is moving from `B` to `A` : velocity of plane along `BA = v cos prop + u cos` `theta` and for no drift from line `AB`. `v sin prop = u sin theta` `rArr sin prop = (u sin theta)/(v) rArr prop = prop'` Time taken from `B` to `A` : `t_(B A) = (l)/(v cos prop + u cos theta)` Total time taken `= t_(A B) + t_(B A)` `= (l)/(vcosalpha - cosalpha) + (l)/(vcosalpha + ucosalpha)` =`(2vlcosalpha)/(v^2 cos^2 prop + u^2 cos^2 theta) = (2 v l sqrt(1 - (u^2 sin^2 theta)/(v^2)))/(v^2 - u^2)`. ,.