# Homework Help: Vector Problem

1. Dec 10, 2009

### O0ZeRo00

An airplane flies due north at 220 km/h relative to the air. There is a wind blowing at 55 km/h to the northeast relative to the ground. What are the plane's speed and direction relative to the ground?

I started by using the law of Cosines.
a^2 = b^2 + c^2 - 2bccos(a)
That's the only thing I could think to try.

2. Dec 10, 2009

### ideasrule

Have you tried drawing a vector diagram?

3. Dec 10, 2009

### itr

first, make a diagram of the thing on the cartesian plane...assume the wind is blowing 45 degrees east of north...draw in the magnitudes(the speed). figure out the other leg when you drop it down to the x axis...if you know what i am talking about. see where that takes you

4. Dec 10, 2009

### O0ZeRo00

Yes, I have. Which is where I got the idea for the Law of Cosines.

5. Dec 10, 2009

### ideasrule

Oh, ok. You can use the law of cosines to figure out the magnitude of the resultant vector, but it's easier to add the x and y components of the two velocity vectors to get the x and y components of the resultant velocity vector.

6. Dec 10, 2009

### O0ZeRo00

Okay. I've solved it. It was 271.79 Km/h at 8.54 degrees east of north.
Thanks for your help.
:]

7. Dec 10, 2009

### itr

if you make the diagram....and add the 2 velocity vectors...you end up with....

220sin90 y(hat) + 220cos90 x(hat)
55sin45 y(hat) + 55cos45 x(hat)

add them up using the x and y components as variables....getting a total of...
258.9 y(hat) + 38.9 x(hat)

Your resultant vector is absolute value of R = square root of x^2 + y^2
this will get you your magnitude of 261.8. so this is the final speed.

THen to get the angle it is going.....do arc tan of y/x...so 38.9/258.9
you get it will be heading 8.5 degrees east of north.

for some reason i dont like that answer all to much...maybe someone can check me on it but that is how you do it

Last edited: Dec 10, 2009
8. Dec 10, 2009

### O0ZeRo00

Well, I know it's correct because I submit my answers onto a website that checks to see if it's right or not.

9. Dec 10, 2009

### itr

I sent in mine before i saw your answers....so. did you check your velocity? i double checked mine and it seems to come to the same every time...yours is right says your website?

10. Dec 10, 2009

### O0ZeRo00

Hmm... That's odd because mine comes out right too.

11. Dec 10, 2009

### O0ZeRo00

Ahh! Nevermind. Typo. Mine actually was 261.79. My bad. Ha.

12. Dec 10, 2009

### itr

oh well...its been awhile since i got my lesson on vector addition so i would take yours hehe. feel free to help me with my current vector problem locatedo n the front page of the forums haha