Physics

An airplane is flying due south with a velocity of 26.0 m/s.
a. If there is a tailwind of 27.0 m/s, what is the magnitude and direction of the actual velocity of the airplane? (a tailwind blows in the same direction as the motion of the airplane)
b. If there is a headwind of 27.0 m/s, what is the magnitude and direction of the actual velocity of the airplane? (a headwind blows across the direction and motion of the airplane)
c. If there is a crosswind of 27.0 m/s blowing due west, what is the magnitude and direction of the actual velocity of the airplane? (a crosswind blows across the direction and motion of the airplane)

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  1. 26 m/s is about 10% from stalling for a Cessna 150.
    With a tailwind, the airspeed does not change, but it will be added to the ground speed ("actual velocity").
    With a headwind, the airspeed does not change either, but it will be subtracted from the ground speed.

    Funny it may seem, with the headwind, the given aircraft is actually going backwards!

    Wind is rarely in the same direction as the aircraft's velocity (as in (a) an (b)), so that in general, wind speed is added to the ground speed vectorially.
    Airspeed: <0,-26>
    wind speed: <-27,0>
    ground speed: <-27,-26>
    Magnitude: √(27²+26²)= 37.48 m/s
    Direction (CCW from east):atan(-26/-27)=223.9°

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