Solving 2D Motion Problem: A to B Flight Distance

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Homework Help Overview

The problem involves calculating the direct flight distance from airport A to airport B after an airplane follows a specific path involving multiple segments of flight. The subject area pertains to 2D motion and vector resolution in physics.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculation of vector components and the application of the Pythagorean theorem. There are questions about the accuracy of the components derived from the given angles and distances.

Discussion Status

Some participants have offered insights into potential errors in component calculations, while others suggest graphical methods as a means to verify results. There is acknowledgment of confusion regarding angle interpretation and sign conventions in trigonometric calculations.

Contextual Notes

Participants note the complexity introduced by the "west of north" angle and the importance of correctly identifying vector components. There is a mention of a specific online homework platform that may have its own answer key, which adds to the pressure of finding the correct solution.

Aubiefan
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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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