A person travelling east wards at the rate of ` 4 km h^(-1)` finds that the wind seems to blow directly from the north . On doubling its speed, the wind appears to come from ` 45^@` north of east. Find the actual velocity of the wind.

Explanation

Absolute velocity, i.e., velocity with respect to the ground. Let the velocity of wind w.r.t. the ground is `u`.
Case I:



`u sin theta-4=0`
`usin theta=4......(i)`
Case (II)

`tan 45^(@)=(usin(90+theta))/(8+ucos(90+theta))=(ucos theta)/(8-u sin theta)`
`1=(u cos theta)/(8-4) implies u cos theta=4.......(ii)`
Wind is blowing with a speed of `4sqrt(2) km//h` and blowing in south-east direction.