Calculating Resultant Velocity of Airplane in Different Wind Conditions

AI Thread Summary
To calculate the resultant velocity of an airplane flying at 200 km/h with a 50 km/h tailwind, the groundspeed increases to 250 km/h due to the wind aiding the plane's motion. Conversely, with a 50 km/h headwind, the groundspeed decreases to 150 km/h as the wind opposes the plane's velocity. Understanding the distinction between airspeed and groundspeed is crucial, as the latter is influenced by wind conditions. Vector addition is necessary for accurate calculations, considering the direction of the wind relative to the airplane's flight path. Proper application of these principles allows for effective analysis of an airplane's performance in varying wind conditions.
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Homework Statement



**calculate the resultant velocity of an airplane that normally flies at 200km/h if it encounters a 50km/h tailwind. IF it encounters a 50km/h headwind.

its obvious that each would either slow down the plane or speed it up but i don't know how
 
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Just remember that there are two speeds for a plane -- the airspeed and the groundspeed. The groundspeed would be dependent on the airspeed (the speed the plane sees itself going through the air) and the speed of any wind.
 
The tail wind is flowing in the direction of the plane, and the head wind comes directly at the plane, i.e. the wind flows in the opposite direction of the plane's velocity.

Simple addition would require simply adding the corresponding components of each vector. The coordinate system is important therefore.

See this for reference on basic vector operations:
http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html
 

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