An aeroplane has to go from a point `O` to another point `A`, at distance `d` due `37^(@)` east of north. A wind is blowing due north at a speed of `20 m//s`. The air speed of the plane is `v`. (a) Find the direction in whihc the pilot should head the plane to reach the point `A`. (b) Find the time taken by the plane to go from `O` to `A`.

Explanation

(a) If a particle moves in a straight line, the velocity of particles, perpendicular to straight line should be zero. If an aeroplane moves along `OA`, the pilot should head the plane towards right of line `OA`.
`_|_^(ar)` to line OA:
`v sin theta=20 sin 37^(@) =12`
`sin theta=12/v`
`theta=sin^(-1)(12/v)`
The pilot should head the plane at angle
`sin^(-1) (12/v)` east of line `OA`,
(b) Along line `OA`:
Time taken by the plane to move from `O` to `A`:
`t=d/(20cos 37^(@)+v cos theta)=d/(16+v cos theta)`