# Help! how do i find displacement of two vectors?

1. Oct 7, 2007

### pebbles

it's been driving me crazy all day! what do i do if i have the length of two vectors and one angle?! what if i don't have an angle?!

2. Oct 7, 2007

### Gannon

What do you mean exactly by "one angle"? Do both vectors have the same angle? By "not having an angle," do you mean lying on an axis?

3. Oct 7, 2007

### pebbles

here's an example problem:

a plane goes 29 meters north, and then changes direction to go east at 35 degrees for 50 meters

Last edited: Oct 7, 2007
4. Oct 7, 2007

### Gannon

Ah, ok. All you have to do is break apart the 2nd vector into its x and y components. You can do that with the equations x = rcos$$\theta$$ and y = rsin$$\theta$$. This turns the vector at an odd angle into a horizontal and vertical pair of vectors, which can then be easily dealt with as a problem you have probably done before. Just remember that vectors along the same line add together.

5. Oct 7, 2007

### pebbles

the problem i gave, are the vectors on the same line?

how would i go about the problem if they were not?

how would i do this without an angle?

i truly appreciate the help. i'm reviewing for an exam, and i have many questions swirling in my brain right now.

Last edited: Oct 7, 2007
6. Oct 7, 2007

### pebbles

ok, since you said you add them if they are on the same line, if i go, say 50 meters south, then back track and go 20 north, would i add 50 and 20? or would i subtract 20 from 50, because that would be my final position....

i understand displacement to be final position minus initial position, does this apply to vectors?

7. Oct 7, 2007

### Gannon

Yes; vectors act the same way as distance, except along with magnitude, you must take direction into consideration. In your example, you are adding 50 miles and -20 miles (if you designate north as negative).

In your main question, after getting your components, you will have your 1st vector north along with a component vector also north. Since these are both in the same direction, they add together. You are then left with a larger north vector and the other component vector that is pointed east.

EDIT: Hmm... my previous statement depends on the angle's point of reference. I assumed you meant 30 degrees north of east.

Last edited: Oct 7, 2007
8. Oct 7, 2007

### pebbles

in my "back tracking" example, which direction would i take? would the answer be 30 going south?

i'm still a little unclear about my main question.

"a plane goes 29 meters north, and then changes direction to go east at 35 degrees for 50 meters"

rx=50cos35
ry=29sin35
?

9. Oct 7, 2007

### pebbles

oh wait, you said the second vector, so rx=50 cos 35 and ry=50 sin 35?
i'm confused.

10. Oct 7, 2007

### Gannon

Yes, that's exactly right. I threw together a picture to help explain.

http://i57.photobucket.com/albums/g231/Paylardo/vectors.jpg

1: The vectors as described (forgot to put in the angle, but it's there).

2: The second vector has been broken into its x and y components.

3: Vectors in the same direction are added together. In this case, the two "north" vectors add while the "east" vector does not change.

4: An approximate displacement. Actually, the final vector would point a bit more toward east.

Finally, to get the product of this whole deal (shown in step 4) you need to resolve the vectors in step 3 (notice that you now have another pair of horizontal and vertical components!).

I don't have any more time to help you out, so if you need help getting from step 3 to step 4, look at the link below under Magnitude and Direction from Components. Take note of the equations near the diagram for magnitude and angle.

http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html

Last edited: Oct 7, 2007
11. Oct 7, 2007

### pebbles

Gannon, i greatly appreciate all that you have done!
i will study more later.

thanks a lot! :]