A man travelling towards east at 8km/h finds that the wind seems to blow directly from the north On doubling the speed, he finds that it appears to come from the north-east. Find the velocity of the wind.

Explanation

Velocity of wind relative to man = Actual velocity of wind - Actual velocity of man `" "` (i)
Let `hati and hatj` represent unit vectors along east and north. Let the actual velocity of wind be given by `x hati +yhatj`.
In the first case, the man's velocity is `8hati` and that of the wind blowing from the north relative to the man is `-phatj`. Therefore,
`" " -phatj = (xhati +yhatj ) - 8hati " "` [from Eq. (i)]
Comparing coefficients, `x -8 =0, y=-p" "` (ii)
In the second case, when the man double his speed, wind seems to come from the north-east direction, i.e.,

`" " -q(hati +hatj) = (xhati +yhatj) -16hati`
`therefore " "x -16 = -q , y =-q" "` (iii)
Putting x =8, we get `q` =8
`" " y = -8`
Hence, the velocity of wind is `x hati +yhatj = 8(hati -hatj)`
Its magnitude is `sqrt((8^(2) + 8^(2))) = 8sqrt2 and tan theta = -1 or theta = -45^(@)`
Hence, its direction is form the north to the west.