# Addition and Subtraction of Vectors

#### MuchJokes

A plane, travelling with a velocity relative to the air of 320km/h [28 S of W], passes over Winnipeg. The wind velocity is 72km/h . Determine the displacement of the plane from Winnipeg 2.0 h later.

Cosine Law -> c^2 = b^2 + a^2 - 2*b*a*Cos<C
Sine Law- (Sin<A)/a = (Sin<B)/b = (Sin<C)/c

West is left, South is down.
1. Drew the thing. It was pretty.
2. Drew a line parallel to West and found part of the really big angle. Then I added 90 to it. = 118 degrees
3. Used Cosine law to get resultant Velocity
4. Used Sine law to get the top little angle. Added it to the existing 28 degrees to get my resultant angle S of W
5. Burst into tears because the answer in the book brutally murdered my already low self-esteem.

Last edited:
Related Introductory Physics Homework News on Phys.org

#### lavalamp

It would help if you show your working out, so that it's possible to determine at what point you made a mistake.

It certainly sounds like you know what you're doing since you're going about it in the right way.

#### MuchJokes

Here's what it looks like.

I used to Cosine law to find the resultant Velocity, and then used the sine law. Unfortunately, my answer for the top angle was 10 degrees. Which apparently is wrong.

#### Attachments

• 5.3 KB Views: 314

#### lavalamp

I can't look at that attachment until it has been approved by a moderator. Can you put it online somewhere? Any random image host would do.

Edit: I also get 10.19 degrees for the small angle in the triangle. But remember that needs to be added on to the 28 degrees to get the angle south of west.

Last edited:

#### MuchJokes

http://img227.imageshack.us/img227/4299/physicswa9.jpg [Broken]

I know this is against the rules but the book says the answer is 30 degrees S of W

Is this just wrong or something? Or does something change from the transition from velocity to displacement?

Last edited by a moderator:

#### lavalamp

It seems as though the book may just be wrong. However go back and check, double check, triple check the question to make sure there's no information you missed or read incorrectly.

If you can't find anything that changes the answer, you might want to mention this to the teacher. And if it turns out that the answer is actually 30 degrees south of west, make sure you find out what you did wrong, then come back and tell me too.

#### MuchJokes

There went my monday. Thanks for the help.

#### lavalamp

Heh, I can sympathise, but at least you got it right. It's better than spending lots of time on it and still getting it wrong.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving