1. ## Vectors and Velocity

A plane heads on a bearing of 210 degrees at 500 mph; the winds at the cruising altitude are 75 mph from the southwest to the northeast.

Write the vector u representing the velocity of the plane relative to the air and the vector v representing the velocity of the wind.

2. If I worked this out correctly, I think vector u = <-250√3,-250>
and vector v = <-75,0>.

Is this right?

3. Originally Posted by Sky
A plane heads on a bearing of 210 degrees at 500 mph; the winds at the cruising altitude are 75 mph from the southwest to the northeast.

Write the vector u representing the velocity of the plane relative to the air and the vector v representing the velocity of the wind.

this really is not a good venue for teaching ... hopefully you have been taught the basics.

start by making a sketch ... note that the directions are more than likely referenced to true north.

Air vector + Wind vector = Ground vector

you can manipulate vectors using the law of sines/cosines or by using components.

4. Here is my sketch:

Upon further evalution, this seems to be incorrect. Ugh.

5. 3 digit bearings are usually measured clockwise from true north ... otherwise, the problem usually uses the 30 degrees west of south type of description.

6. Whoops.
Here we go?

7. ok ... u and v = ???

8. u = <-250,-250√3>
v = <-75,0>

?

And the ground vector = <-325,-250√3> ?

9. vector v (the wind vector) blowing NE at 75 mph ...

$\vec{v} = \left<\dfrac{75\sqrt{2}}{2},\dfrac{75\sqrt{2}}{2}\ right>$

10. Ah. Okay.

So, in turn, the ground vector would equal <-197,-380> ?

11. Originally Posted by Sky
Ah. Okay.

So, in turn, the ground vector would equal <-197,-380> ?
come on ... you can add components as easily as I can.

12. Originally Posted by skeeter
come on ... you can add components as easily as I can.
I'll take that as a yes.
Thanks