Help how do i find displacement of two vectors?

[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?!

 

[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?

 

[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

 

[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.

 

[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.

 

[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?

 

[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.

 

[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
?

 

[pebbles]

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

 

[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

 

[pebbles]

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


thanks a lot! :]