# Homework Help: Physics-Vectors Homework Help

1. Jan 27, 2010

### bluefire90

Two airplanes taxi as they approach the terminal. Plane 1 taxies with a speed of 11.3 m/s due north. Plane 2 taxies with a speed of 7.6 m/s in a direction 22.2° north of west. What is the direction of plane 1 relative to plane 2? Give the angle counterclockwise relative to the north. What is the direction of plane 2 relative to plane 1?

*I solved for magnitude first then velocity*

What is the magnitude of the velocity of plane 1 relative to plane 2?

To solve for the magnitude I found the vector components of plane 2:

Y component: 7.6 * sin(22.2°) = 2.87 m/s
X component: 7.6 * cos(22.2°)= 7.04 m/s
To find the final magnitude of the resultant vector I just used the pythagorean theorem after subtracting the plane 1 components FROM the plane 2 components.

2.87 m/s - 11.3 m/s = -8.43 m/s
7.04 m/s - 0 m/s = 7.04 m/s

Now to find the magnitude I used the pythagorean theorem.
Using the pythagorean theorom I got 10.98m/s as the relative velocity. This velocity is the same for plane 2 relative to plane 1.

To find the direction of plane 1 to plane 2 I just used the arctan formula

arctan (7.04/-8.43) = -39.86°
Now since its counterclockwise from north I just added to 360 to get 320° which is the correct answer.

I can't seem to figure out how to get the direction of plane 2 relative to plane 1 however and I've tried using the law of cosines and various other methods but I'm not sure where to go. Any help would be appreciated.

2. Jan 27, 2010

### tiny-tim

Welcome to PF!

Hi bluefire90! Welcome to PF!

And the direction of plane 2 relative to plane 1 is just the opposite of the direction of plane 1 relative to plane 2 (V21 = -V12).

So the opposite of 320º is … ?

3. Jan 27, 2010

### bluefire90

Thanks for the help! Although I did try -320.0° and it wasn't correct! I thought the same thing though

4. Jan 28, 2010

### tiny-tim

There's no such thing as -320º … that would be 40º

but that isn't the opposite of 320º anyway, is it?

(just draw it! )

5. Jan 28, 2010

### bluefire90

Haha my background in geometry is pretty weak but if I looked at it logically and drew it the opposite might be 130?

6. Jan 28, 2010

### bluefire90

140 degrees i mean

7. Jan 28, 2010

### tiny-tim

Help! You're confusing me!!

Yes, the opposite angle is always the original ± 180º.

8. Jan 28, 2010

### bluefire90

haha thanks for the help! Wow that problem just made a lot more sense!