Why is this incorrect? (Two-dimensional motion problem)

[frankfjf]

Alright, here's the problem I need help with:

A watermelon seed has the following coordinates: x = -7.2 m, y = 1.4 m, and z = 0 m. Find its position vector as (a) a magnitude and (b) an angle relative to the positive direction of the x axis. If the seed is moved to the xyz coordinates (5.9 m, 0 m, 0 m), what is its displacement as (c) a magnitude and (d) an angle relative to the positive direction of the x axis?

Parts a through c I've solved and have correct, but my answer to d is being rejected. I don't understand why.

For a I got 7.3m.

For b I got 169 degrees.

For c I got 13.2m.

However, for d I get 174 degrees, but that's wrong. I used the same proceedure for part b and got that right though! Could someone explain why please?

Thanks in advance!

 

[Doc Al]

What are the x & y components of the displacement?

 

[frankfjf]

For the first two parts, the components are of course as listed.

For the latter two parts, I obtain 13.1 for the x component, and -1.4 for the y component.

 

[Doc Al]

I obtain 13.1 for the x component, and -1.4 for the y component.

Good. So how did you get your answer of 174 degrees?

 

[frankfjf]

I take the inverse tangent of -1.4/13.1.

Then I add 180 to it since it satisfied the first answer. Though admittedly I'm not sure why this is so. I originally thought adding 90 degrees to both would suffice, since isn't the first quadrant in the positive x axis?

 

[Doc Al]

Rather than try to apply some memorized rule, just draw yourself a picture. Identify the triangle involved, find its angle (using inverse tangent), and then translate the answer to an angle with respect to the +x axis. That way you'll be sure of your answer.

 

[frankfjf]

Ah-ha! I see what you mean. The first one needed to be adjusted to get there, but the second one doesn't, so I left it at -6.1 degrees and that was correct.

 

[Doc Al]

Now you're thinking.