Understanding Relative Angles in Navigation: Solving Confusion with Terminology

[frankfjf]

If someone wants an angle that is relative to north with east of north positive and west of north negative, what does that mean? Is that the positive x axis? My guess is the positive y axis, since 90 degrees would have those conditions, but not sure..

Here is the problem that's brought up this confusion:

A train at a constant 75.0 km/h moves east for 39 min, then in a direction 42.0° east of due north for 13.0 min, and then west for 69.0 min. What are the (a) magnitude and (b) angle (relative to north, with east of north positive and west of north negative) of its average velocity during this trip?

I have a, which is 14.6 km/h.

But for b I get an angle of -24.6 (x component = -13.3, y component = 6.1).

I have no idea how to adjust the angle, -24.6, to satisfy b. My only idea is to draw it and adjust from there, but I first need to know where exactly they want the equivalent angle, which I don't understand from their wording.

 

[andrewchang]

the question is just saying that the angle would be positive if you gave it east of north, or alternatively, you could give it as negative if it were west of north.

 

[frankfjf]

Then I'm at a loss. Why is -24.6 wrong? It's in quadrant 2, west of north, and is negative.

 

[frankfjf]

This is driving me crazy. What am I doing wrong?

 

[cepheid]

What leads you to believe that it is wrong? If the x component is negative and the y component positive as you claim, then the vector is pointing west of north, which the problem wants you to treat as negative.

 

[frankfjf]

Well, my magnitude is correct, so my x and y components must be correct, but for some reason the online quiz is rejecting -24.6 as the answer to b.

 

[chroot]

Are you using the correct number of significant digits?

- Warren

 

[frankfjf]

The quiz says that significant digits are disabled, with a tolerance of +/-2%.

The full number my calculator gives is -24.63839672.