A light plane is headed due south with a speed relative to still air of 280 km/h. After 1 hour, the pilot notices that they have covered only 150 km and their direction is not south but southeast. What is the wind velocity?
Find the magnitude (km/h) and angle (° north of east).
Let us assume the wind velocity be v km/h in a direction at an angle Q(read as theta) north of east.
velocity of plane in south direction,
vs = 280 - v*sin(Q) ........(1)
and the velocity in the east direction,
ve = v*cos(Q) ...
This solution is provided in 266 words. It calculates velocity and net velocity and uses these equations to find magnitude and velocity of the wind.