Vector Addition and Flight Planning

[SirMarksAlot]

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.

 

[Delphi51]

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.

 

[SirMarksAlot]

i was wondering if this diagram was correct?

 

[Delphi51]

No, it should be like this:

The red airspeed plus the windspeed adds up to a vector going at the desired angle 30 degrees E of N (groundspeed).

 

[SirMarksAlot]

kk thank you, no wonder i kept getting the wrong answer