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 `10 ms^(-1)`. The air speed of the plane is v. (i) Find the direction in which the pilot should head the plane to reach the point A. (ii) Find the time taken by the plane to go from O to A.

Explanation

(i) If a particle moves in a straight line, the velocity of particle perpendicular to straight line should be zero. If an aeroplane moves along OA, the pilot should head the plane towards right of line OA.

Perpendiclar to line OA
`v sin theta = 10 sin 37^(@) = 6`
`sin theta = (6)/(v) rArr theta = sin^(-1)((6)/(v))`
The pilot should head the plane at angle
`sin^(-1)((6)/(v))` East of line OA
(ii) Along line OA

Time taken by the plane to move from O to A
`t=(d)/(10 cos 37^(@)+v cos theta)=(d)/(8+v cos theta)`