# Vectors and Velocity

• Mar 20th 2011, 05:11 PM
Sky
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.

• Mar 20th 2011, 05:33 PM
Sky
If I worked this out correctly, I think vector u = <-250√3,-250>
and vector v = <-75,0>.

Is this right?
• Mar 20th 2011, 05:44 PM
skeeter
Quote:

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.
• Mar 20th 2011, 05:55 PM
Sky
Here is my sketch:

http://i11.photobucket.com/albums/a1...e/Airplane.jpg

Upon further evalution, this seems to be incorrect. Ugh.
• Mar 20th 2011, 06:11 PM
skeeter
3 digit bearings are usually measured clockwise from true north ... otherwise, the problem usually uses the 30 degrees west of south type of description.
• Mar 20th 2011, 06:19 PM
Sky
• Mar 20th 2011, 07:13 PM
skeeter
ok ... u and v = ???
• Mar 20th 2011, 07:39 PM
Sky
u = <-250,-250√3>
v = <-75,0>

?

And the ground vector = <-325,-250√3> ?
• Mar 20th 2011, 07:47 PM
skeeter
vector v (the wind vector) blowing NE at 75 mph ...

$\vec{v} = \left<\dfrac{75\sqrt{2}}{2},\dfrac{75\sqrt{2}}{2}\ right>$
• Mar 20th 2011, 07:52 PM
Sky
Ah. Okay.

So, in turn, the ground vector would equal <-197,-380> ?
• Mar 20th 2011, 08:00 PM
skeeter
Quote:

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.
• Mar 20th 2011, 08:05 PM
Sky
Quote:

Originally Posted by skeeter
come on ... you can add components as easily as I can.

I'll take that as a yes.
Thanks