The Plane and The Wind
Observe the three planes in the picture below. Each plane is heading south with a speed of 100 mi/hr. Each plane flies amidst a wind which blows at 20 mi/hr. In the first case, the plane encounters a tailwind (from behind) of 20 mi/hr. The combined effect of the tailwind and the plane speed provide a resultant velocity of 120 mi/hr. In the second case, the plane encounters a headwind (from the front) of 20 mi/hr. The combined effect of the headwind and the plane speed provide a resultant velocity of 80 mi/hr. In the third case, the plane encounters a crosswind (from the side) of 20 mi/hr. The combined effect of the headwind and the plane speed provide a resultant velocity of 102 mi/hr (directed at an 11.3 degree angle east of south). These three resultant velocities can be determined using simple rules of vector addition. In the case of the crosswind, the Pythagorean Theorem and SOH CAH TOA are utilized to determine the magnitude and the direction of the resultant velocity.
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The Effect of Wind
When you’re flying a plane, you have to deal with wind. You may encounter a side wind to blow you off course, a tail wind to speed you up by blowing in the direction the plane is moving, or a head wind to slow you down by blowing opposite to the direction the plane is moving. Headwinds get you to your destination more slowly, and tailwinds will get you there faster.
Thankfully, the cockpit is full of instruments that tell you about your motion, including one that tells you the speed that the plane is moving. To be more exact, it tells you the speed of the plane relative to the surrounding air. This isn’t really the same thing as how fast the plane is moving, though. Why? Well, the air itself can also be moving. If the air is moving east at 70 mph, and the plane is moving at 150 mph relative to the air (this number is called the relative wind ), your instruments will say 150 mph, but the plane will be moving at 220 mph relative to the ground. Any motion the plane is undergoing relative to the air has to be added to the motion of the wind to figure out how the plane is really moving.
A wind pointing to the side can cause you to drift off course, so the plane’s direction must be adjusted to keep it moving along the right path despite the wind.
Airspeed instruments measure your speed relative to the surrounding air, not relative to the ground 
Before we get into some of the more complex ways air motion affects the way you fly a plane, we need to define a few terms. The airfoil is any surface that produces more lift (upwards force) than drag (backwards force) when passing through the air. Airfoils include the wings that lift the plane, fins that add stability, and flaps that control the plane.
If you draw a straight line from the leading edge of the wing (airfoil) to the trailing edge, that line is called the chord line . In some planes this line points straight forward towards the front of the plane, but it can also point slightly up. The angle between this line and the overall direction the air is moving across the plane (including wind speed) is called the angle of attack .
Diagram showing relevant terms 
When you’re high in the sky, the wind tends to blow in a steady direction, only changing gradually, so major adjustments because of the wind are not usually needed. However, changes still need to be made now and again, and pilots should always take the wind into account when turning or changing the altitude of the plane.