## nath 3 years ago Consider a particle with initial velocity that has magnitude 12.0 m/s and is directed 60.0 degrees above the negative x axis. What is the x component Vx of V? What is the y component Vy of V?

1. Hunus

|dw:1329692762479:dw| The x component Vx of V is the velocity vector V projected onto the x axis. We obtain this magnitude as follows $v_{x}=12\cos(120)=-12\cos(60)=-12(\frac{1}{2})=-6$ The y component Vy of V is the velocity vector V projected onto the y axis. We obtain this magnitude as follows $v_{y}=12\sin(120)=12\sin(60)=12\frac{\sqrt{3}}{2}=6\sqrt{3}=10.4$ |dw:1329693129338:dw|

2. nath

why does sin have a positive value?

3. Hunus

y has a positive value in the top two quadrants

4. Hunus

|dw:1329693437661:dw|

5. nath

so to figure out positive and negative i have to look at 12

6. Hunus

You have to look at the direction it's pointing in. For theta equal to 120 or '60 above the negative x axis' the vector is pointing in the negative x direction and in the positive y direction

7. nath

so what is u have something like this :

8. nath

srry i mean

9. nath

|dw:1329693963427:dw|

10. nath

now its moving clockwise

11. Hunus

The vector A you described is at an angle of (180+60) 240 degrees with respect to the positive x axis as you can see from your picture it is directed toward the negative x negative y direction, so both x and y will be negative.

12. nath

why do i have to add 180?

13. Hunus

|dw:1329694073557:dw| Because we're making the angle with respect to the positive x axis to make it simple to take the sine and cosine of the vector

14. Hunus

By adding 180 to 60 we're changing it from your original picture |dw:1329694180018:dw| and making it |dw:1329694218137:dw|

15. nath

or u can say the angle is -60

16. Hunus

If we're taking it to be with respect to the positive x axis |dw:1329694331261:dw| then it would be -120 degrees. -60 degrees looks like this |dw:1329694414386:dw|

17. nath

|dw:1329694584288:dw|

18. nath

thats how u show it

19. nath

cause its moving clockwise

20. Hunus

Yes.

21. nath

so in this question is the 60 degrees going clockwise

22. Hunus

It typically doesn't matter how you arrive at the angle, but it appears that the angle was rotated counter clockwise 60 degrees. The vector is at 240 degrees with respect to the positive x axis.

23. nath

so qhen do i know when to add 180 or minus 180

24. Hunus

Look at the positive x axis and see how many degrees it takes to get to your vector. This is only showing whether a vectors components are positive of negative.

25. Hunus

or negative*

26. nath

can u please give me an example of each type if itsnt too much trouble

27. Hunus

|dw:1329695075597:dw| Is vector M's x component positive or negative? What about its y component?

28. nath

the x compoinent is negative while the y component is positive

29. Hunus

$v_x=|M|\cos(150)=|M|(\frac{-\sqrt{3}}{2})=\frac{-|M|\sqrt{3}}{2}$so we know that the value of Vx is negative while the value of Vy is positive. From this we could say that $v_{y}=|M| \sin(30)=\frac{|M|}{2}$ and $v_{x}=-|M|\cos(30)=-|M|\frac{\sqrt{3}}{2}$ Where |M| is the magnitude of the vector M However we could also say that, to get to vector M from the positive x axis |dw:1329695464157:dw| we would have to go through an angle of 150 degrees. Thus would make our calculations $v_y=|M|\sin(150)=\frac{|M|}{2}$ As you can see we arrive at the same answer which is why it doesn't matter which way you get to the angle.

30. Hunus

$v_{x}=|M|\cos(150)=|M|(\frac{-\sqrt{3}}{2})=\frac{-|M|\sqrt{3}}{2}$

31. nath

what does 150 degrees tellus ?

32. nath

are we saying the angle 150 is equal to 30 degrees

33. Hunus

150 degrees tells us what the angle is from the positive x axis. That's what we usually like to use as a reference point when using sines and cosines.

34. Hunus

What we are saying is that we only need the reference angle (how many degrees it is from the closest x axis) if we know if x is positive or negative or y is positive or negative

35. nath

so basically we are saying the angle is 150 degrees away from the orgin

36. Hunus

From the positive x axis

37. nath

what about the negative x axis

38. Hunus

150 degrees tells us how far we would have to rotate a vector from the positive x axis (0 degrees) to get to where the vector is.

39. nath

ohhh i get it

40. Hunus

Good :)

41. nath

and to find the negative value what would i have to do

42. Hunus

Well, the degrees from the positive x axis tells us whether it's positive or negative. For example, between 0 and 90 degrees, x and y are negative, between 90 and 180 degrees x is negative and y is positive, between 180 and 270 degrees both x and y are negative and from 270 to 360 degrees x is positive and y is negative. If you, for example, put in 6sin(340) you will get a negative value because y is negative in that quadrant. If you put in 12cos(320) you will get a positive value because x is positive in that quadrant.

43. Hunus

between 0 and 90 x and y are positive*** sorry

44. nath

so it doesnt matter whether u say 30 degreees or 150 degrees

45. nath

46. Hunus

It matters, but only as far as the dirrection goes. This is because the MAGNITUDE of cos(30) is the same as the MAGNITUDE of cos(150), but one is negative and one is positive

47. Hunus

Sorry for the delay on that response

48. nath

and that has to do withe quadrant whether is positive or negative