Who knows how to add vectors?

Hello there. This week in class we have been learning how to add vectors, and let me tell you, its actually not that hard once you get your head wrapped around the concept and you do a lot of questions. Here is a question that was on the green sheet Mr. Chung gave us.

A+D
The first thing you do is to draw the direction of the positive arrows. It should look like this.

Then you need to figure out the values for x and y of the diagonals.
Ax+Ay+Dx+Dy
= Ax+Dx + Ay+Dy
= 11.5km[E] + 18km[W] + 9.6km[S] + 1.6km[N]
11.5 and 18 represent Rx and 9.6 and 1.6 represent Ry
A simple way to add these together is to add the directions opposite of each other together. First you have to turn them into one unit. For example, going a certain distance towards North is the equivalent of going that same distance South, because they will cancel each other out. The same with going a certain distance East and going back the same distance West. In this case, if you want to add 11.5km[E] + 18km[W] , you need to subtract 18km[W] from 11.5km[E] and keep the [W] sign.
The answer would be Rx= 6.5km[W].
You could also subtract the East direction from the West, but then would have to keep the East sign.
Similarly, you would do the same for North and South.
9.6km[S] + 1.6km[N]
= 1.6km[N] - 9.6km[S]
= -8
Ry= 8km[S]
(Keep in mind that the negative sign does not change the number, it simply shows the direction. If it is negative, it means it is going in the opposite direction)

You then use the Pythagorean theorem to find the hypotenuse:
R=
R= 10.3

Lastly, you use trigonometry to find the angle.
tanθ =opp/adj
= 6.5/8
θ= tan -1 (6.5/8)
θ = 39˚

You now have all the missing pieces, and need to simply put them together.
R= 10.3 [S 39˚ W]

Here is what the triangle would look like.



-Peggy.