SRAW
Rocket Man

2007 Nov 6 • 2525
601 ₧

sup guys, I have my maths final this wednesday, and there's gonna be stuff on vectors , which I really suck at.

So please halp:
A plane is flying due east at 200mph when it encounters a wind W = 30i + 40j
a. What is the path of the plane in this wind if the pilot keeps it pointed east?

This one was easy, just <200,0> + <30,40> = <230,40>

BUT I have no idea how to do b :(

b. What direction should the pilot point the plane in order to fly due east?

The answer in the back of the book says 11.5 degrees south of east, but I have no idea how to get it. So please help :(

Down Rodeo
Cap'n Moth of the Firehouse


2007 Oct 19 • 5486
57,583 ₧

How much trigonometry do you know? You need to create a component of velocity exactly equal to the velocity of the wind, but opposite. If I could be bothered I'd draw a picture.

Drawing pictures always helps.

Also, THIS was your best hope for getting maths help?!

SRAW
Rocket Man

2007 Nov 6 • 2525
601 ₧

After playing around with my calculator, I finally solved it.
Basically, the vector going down was <200,-40>, or whatever something, then you did some inverse tangent of it and I got 11.5 woohoo. And here's another question, when they ask to find the angle between a vector and an axis, is it ok to take the axis as a unit vector (ie: <0,0,1> , <1,0,0>) and calculate using that cos x = dot product/magnitude, or do we just have to draw a triangle and calculate? Cause my teacher really sucks and never explains this stuff

Down Rodeo
Cap'n Moth of the Firehouse


2007 Oct 19 • 5486
57,583 ₧

Yes, the calculation is independent of the size of the vector. If you think about it, it has to be! See if you can work out why (and how it works) :)

SRAW
Rocket Man

2007 Nov 6 • 2525
601 ₧

Well my exam just finished and thankfully no word problems, and the test was really easy too, and also to get a 4.0 for this class you need a 93% up, cuz apparently it's that hard or something. But of course, SRAW being SRAW, I had a 99.6% up to the final, so yeah. I WIN.

SRAW
Rocket Man

2007 Nov 6 • 2525
601 ₧

and yeah, I now realize why it is independent of the size, so that's awesome