Vector Addition and Flight Planning

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Homework Help Overview

The discussion revolves around a flight planning problem involving vector addition, specifically addressing the effects of wind on an airplane's heading and speed. The scenario includes calculating the appropriate heading for the pilot, the duration of the flight, and the impact of wind on flight time.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss two main approaches: using the law of sines and cosines to solve the triangle formed by the vectors, or converting vectors into rectangular components to analyze the x and y components separately. One participant seeks validation for their diagram, while another provides a correction regarding the vector addition.

Discussion Status

The discussion is ongoing, with participants exploring different methods to approach the problem. Some guidance has been offered regarding the correct vector representation, but there is no explicit consensus on the solution yet.

Contextual Notes

Participants are working within the constraints of the problem statement, which includes specific distances, angles, and wind conditions. There is an indication of confusion regarding the diagram and calculations, suggesting that assumptions about vector addition may need clarification.

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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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