An aeroplane flies along a straight path A to B and returns back again. The distance between A and B is 1 and the aeroplane maintains the constant speed v. There is a steady wind with a speed u at an angle thetawith line AB. Determine the expression for the total time of the trip.

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

1.	An aeroplane flies along a straight path A to B and returns back again. The distance between A and B is 1 and the aeroplane maintains the constant speed v. There is a steady wind with a speed u at an angle thetawith line AB. Determine the expression for the total time of the trip.
Answer» Solution :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` totaltime 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))`