Question

Trig help! See attatched

Answer 1

both problems
@IMStuck

Answer 2

Alright so with vectors...each has an x component...and a y component

W can find those by taking the magnitude of the vectors...and multiplying it by cos of the angle and also sin of the angle) (for 'x' and 'y' components respectively)

Answer 3

For example vector 1

\[\large 14cos(118) = \text{x-component}\]
and
\[\large 14sin(118) = \text{y-component}\]

Answer 4

So do the same for the other vector also. Got it. What would I do next?

Answer 5

Because it looks like I need to add and sub them.

Answer 6

And for the v1 + v2 we are adding the vectors and also subtracting them...

to do that we merelyadd the corresponding components..

we add the 2 x components of the vectors that make up the resulting vector's x-component
and we do the same for the y-components

Answer 7

So what are the components of the 2 vectors we just found?

\[\large V1_x , V1_y, V2_x, V2_y \]?

Answer 8

14cos 118=-6.5726
14 sin 118 =12.3613

Answer 9

22cos217=-17.57
22sin 217=-13.2399

Answer 10

Perfect...so now we write each vector as

\[\large V_1 <-6.5726 , 12.3613>\]
\[\large V_2 <-17.57, -13.2399>\]

Now...to add them simply add the 2 'x' components together....and them add the 2 'y' components together.

Answer 11

Can do!
x=-24.1426
y=-.8786

Answer 12

Great....

So our resulting vector is

\[\large R <-24.1426, .8786>\]

And there you have your 'x' and 'y' components of the resultant vector (what you will write in your table)

Next we just need to find that magnitude and the direction the resultant faces

Answer 13

In order to do that we remember that the magnitude of a vector is found by using

\[\large R^2 = R_x^2 + R_y^2\]
or
\[\large R = \sqrt{R_x^2 + R_y^2}\]

Answer 14

Ok, so let me first do this: you say the resulting vector goes in the diagram box?

The one for first, second, third, and 4th box? I have the + and - ones at the end mixed up.

Answer 15

How do you draw it? I'll come to your r^2 in a sec :) Thanks!

Answer 16

Well we can't do the diagram just yet...we have merely found the components for the resultant so far

but here lets start from the beginning...

diagram of V_1:

Answer 17

The 'x' and 'y' components of V_1 are what we found before

\[\large V1_x = 14cos(118)\]
\[\large V1_y = 14sin(118)\]

and that will complete row 1

Answer 18

Now onto V2

Diagram will be:

Answer 19

and the corresponding x and y components are what we found

\[\large V2_x = 22cos(217)\]
\[\large V2_y = 22sin(217)\]

Answer 20

I'm understanding now!

Answer 21

Now for the adding vectors part...we'll do the diagram first this time

So

We know that the 2 vectors we have so far are:

Answer 22

Well it is important to know the different ways to add vectors...we can add them tip to tail, where you move 1 vector to the tip of the other and find the resultant...



terrible drawing but you get the idea lol