Confused About A Math Problem...

[Staind]

Ok, I'm taking discrete math without any physics background (so we're doing vectors and I'm having trouble understanding the basic concepts).

Anyways, our teacher hasn't really showed us 3D vectors yet but he decided to give us one as a thinking / inquiry problem.

I'm having a little trouble and I was wondering if someone could help me out:

Three forces, each of which is perpendicular to the other two, act on an object. If the magnitues of these forces are 6N, 15N, and 10N respectively, find the magnitude and direction of the resulant. State the angles that the resultant makes with the two larger forces.

Image (sorry for bad paintshop job, I did it rather quickly):
http://www.scmillennium.com/forums/Attachments/math.JPG


Thanks for any support/input,

-Staind.

[Fenguin]

Oooooooo! Math! Are the other two perpendicular?

Since v1 + v2 + v3 = (v1 + v2) + v3,
We first add the 6N and the 15N force. We get a force of magnitude 3 sqrt(29). The angle that it makes with the 15N force is:
tan theta = 6/15
so theta = 21.8 degrees

Then we add the force we just calculated and the 10N force. We get a force of magnitude sqrt(10² + (3 sqrt 29)²) = 19. The angle of that force with the 10N force is
tan theta = 10/3 sqrt 29 so theta = 31.75 degrees

So the resultant force is 19, and the angles are 21.8 and 31.75

Haha, I'm prolly wrong tho :P

[Staind]

According to the back of the book 19N is right, and so is 32DEG but 21 should be a 58 ~~. But I understand it now, thanks.

[Fenguin]

Aww... I got it wrong ;)

[OboeGuru]

Heh, 2/3 ain't bad, that get's you a B in AP Physics!

[Fenguin]

Oh yeah! Crazy grading scale :D

[Exedore]

According to the back of the book 19N is right, and so is 32DEG but 21 should be a 58 ~~. But I understand it now, thanks.

Actually, Fenguin probably just placed a positive axis in the wrong direction, or interpreted the angle from the perpendicular plane. If you account for decimal round-off, 21° and 58° (+ round-off) is 90°, which is just a rotation of one of the axes.

[Luther-Stark]

Gets you a D everywhere else :)

[Fenguin]

:) D's, B's, what's the difference if you turn into a cephalopod the next day? :D

[OboeGuru]

None. But I randomly turn into an arthropod, and let me tell you, those D's really get to ya.

[Fenguin]

Haha, cephalopods can beat arthropods up :D
Aww... arthropods have that pesky armor ;)