Vector Addition and Flight Planning

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SUMMARY

The discussion focuses on calculating the correct heading for an airplane navigating a flight of 1200 km at an angle of 30 degrees east of north, considering a westward wind of 80 km/h and an airspeed of 300 km/h. The solution involves using vector addition, specifically the law of sines and law of cosines, or converting vectors into rectangular components. The correct approach combines the airspeed vector with the wind vector to achieve the desired ground speed. The navigator must adjust the heading to account for the wind's effect on the flight path.

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  • Understanding of vector addition and subtraction
  • Familiarity with the law of sines and law of cosines
  • Knowledge of converting vectors to rectangular components
  • Basic principles of flight navigation
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  • Learn how to apply the law of sines and law of cosines in navigation problems
  • Explore the concept of ground speed versus airspeed in aviation
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Homework Statement



The navigator of an airplane plans a flight from one airport to another 1200 km away, in a direction 30 degrees east of north. The weather office informs him of a prevailing wind from the west, of 80 km/h. The pilot wants to maintain an air speed of 300 km/h.

a) What heading should the navigator give to the pilot?

b) How long will the flight take?

c) How much time did the wind save?


The Attempt at a Solution



I drew the diagram out, but i didnt know how to solve it.
 
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There are two approaches. You can use law of sines and law of cosines to solve the triangle, or you can convert all your vectors to rectangular x and y components and work out the x and y parts separately.
 
Untitled.png


i was wondering if this diagram was correct?
 
No, it should be like this:
plane2.jpg

The red airspeed plus the windspeed adds up to a vector going at the desired angle 30 degrees E of N (groundspeed).
 
kk thank you, no wonder i kept getting the wrong answer
 

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