Solving 2D Motion Problem: A to B Flight Distance

AI Thread Summary
The discussion centers on solving a 2D motion problem involving an airplane's flight path from airport A to B. The user initially struggles with calculating the direct distance from A to B after breaking down the journey into segments. They correctly identified the angle but miscalculated the north and east components, leading to incorrect distance results. After receiving advice to graphically represent the problem and re-evaluate their calculations, the user successfully corrected their components and identified their earlier errors related to the "west of north" angle. The conversation emphasizes the importance of accurate component analysis in solving vector problems.
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I'm having a bit of trouble with this problem, I thought I knew how to solve it but can't get what is listed as the correct answer in the key.

An airplane starting from airport A flies 300 km east, then 410 km at 25.5° west of north, and then 150 km north to arrive finally at airport B.
The next day, a pilot flies directly from A to B in a straight line, what is the distance of this flight?

I was able to find the correct angle, 77.89 degrees north of east, and I tried to use the Pythagorean theorem with the X and Y components to find the length of the resultant, but the website (it's a webassign.net problem for a class) keeps telling me I have the wrong answer. Any insights on what I'm doing wrong? The two answers I keep coming up with are 371.17 km and 333.94 km.

thanks for your time!
 
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You have the wrong E and N components ...
the N component by itself is over 500 km (150 + almost 400).
Show your work!
 
You can do this graphically. Make a drawing to scale, use a protractor also. Then you can tell where your errors lie.
 
Thanks for your advice, I reworked it and found the correct components. I had gotten a little thrown by the "west of north" angle and made a mess of some negative signs when doing the trig.
Thanks again!
 

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