# 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!
Yes, your results look fine.

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!

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Physics Vectors Homework Date
Acceleration Vector Word Problem Mar 19, 2017
Intro to Angled Forces and Vectors question? Dec 2, 2016
Vector Nature pf Projectile Motion Nov 20, 2016
Adding Vectors using Cefore Method Nov 16, 2016