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Study23

  • 2 years ago

Need help with these two vector problems! Given the following x and y components, find the magnitude and direction of the vector, counter clockwise from the x-axis: (1) x comp: -.5, y comp: 1. I found a magnitude of 1.12, but I'm having trouble with the angle. (2) x comp: -1.5 and y comp: -1; I got (1.80, 33.7 degrees, not sure if this is correct, though. I was confused with the negatives and to find the angle.

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  1. ganeshie8
    • 2 years ago
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    mag = \(\sqrt{x^2+y^2}\) angle = \(\tan^{-1} \frac{y}{x}\)

  2. Study23
    • 2 years ago
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    I know, but I'm confused with the "counter clockwise from the x-axis" part of the problem.

  3. ganeshie8
    • 2 years ago
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    angle is always measured in counter clockwise, so dont wry about it

  4. ganeshie8
    • 2 years ago
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    |dw:1381000651274:dw|

  5. ganeshie8
    • 2 years ago
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    btw, ur magnitudes are correct, for angle just plug it in the formula

  6. Study23
    • 2 years ago
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    Is the angle for the second problem correct?

  7. ganeshie8
    • 2 years ago
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    nope

  8. ganeshie8
    • 2 years ago
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    clearly, that 2nd vector is in 4th quadrant, so we shud get angle >180

  9. Study23
    • 2 years ago
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    Hmmm, that's where I'm getting confused

  10. ganeshie8
    • 2 years ago
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    yeah :) just add 180 to that angle, as tan period is \(\pi\)

  11. ganeshie8
    • 2 years ago
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    |dw:1381001032077:dw|

  12. Study23
    • 2 years ago
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    Okay! I just realized as you said that I incorrectly drew the latter problem! The main problem I'm having is the angle for the first problem. When I set it up, (inverse tan) I got a negative angle????

  13. ganeshie8
    • 2 years ago
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    yeah, add 180 to that negative :) whats the big deal !

  14. ganeshie8
    • 2 years ago
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    sorry wait, negative angle is Clockwise, so from positive x direction, it wud be 360-\(\theta\)

  15. ganeshie8
    • 2 years ago
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    |dw:1381001359771:dw|

  16. Study23
    • 2 years ago
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    But how can it be in the 4th quadrant when -.5,1 is in 2nd quadrant?

  17. Study23
    • 2 years ago
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    wouldn't 360--thetha give me an angle over 360?

  18. Study23
    • 2 years ago
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    theta

  19. ganeshie8
    • 2 years ago
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    look at the figure, make out whats happening

  20. ganeshie8
    • 2 years ago
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    |dw:1381001694372:dw|

  21. ganeshie8
    • 2 years ago
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    the whole thing is 360 the vector is \(\theta\) fro positive x-axis clockwise direction

  22. ganeshie8
    • 2 years ago
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    so the vector wud be \(360-\theta\) from positive x-axis counter clockwise direction

  23. Study23
    • 2 years ago
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    Hmmm okay I guess that makes sense. Thank you!

  24. ganeshie8
    • 2 years ago
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    in \(-\theta\), minus just tells us the direction is clockwise

  25. Study23
    • 2 years ago
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    oh okay!!!!

  26. ganeshie8
    • 2 years ago
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    hey wat about this q of urs :- ``` But how can it be in the 4th quadrant when -.5,1 is in 2nd quadrant? ```

  27. Study23
    • 2 years ago
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    ?

  28. ganeshie8
    • 2 years ago
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    |dw:1381001958479:dw|

  29. Study23
    • 2 years ago
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    Yea, its in the 2nd quadrant

  30. ganeshie8
    • 2 years ago
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    angle = \(\large \tan^{-1}\frac{y}{x}\) \(\large \tan^{-1}\frac{-1}{.5}\) \(-63.43\) \(296.57\)

  31. ganeshie8
    • 2 years ago
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    add/subtract 180 to get to 2nd quadrant as tan period is \(\pi\)

  32. Study23
    • 2 years ago
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    So when do I use 180 v 360? Does the counter clock wise from +x affect that?

  33. ganeshie8
    • 2 years ago
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    when the angle is NEGATIVE, that means its measured in CLOCKWISE so subtract it from 360 to get COUNTER-CLOCKWISE

  34. ganeshie8
    • 2 years ago
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    |dw:1381002350796:dw|

  35. Study23
    • 2 years ago
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    And 180?

  36. ganeshie8
    • 2 years ago
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    180 comes from the fact that period of tan is 180 tan(x+180) = tan(x)

  37. Study23
    • 2 years ago
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    But when do you need to add 180?

  38. ganeshie8
    • 2 years ago
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    in this particular case, we clearly knw that the vector is in 2nd quadrant. but when we did the formula we got the angle in 4th quadrant, right ?

  39. Study23
    • 2 years ago
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    yes

  40. ganeshie8
    • 2 years ago
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    since adding/subtracting 180 to tan wont change its value, add/subtract 180 to get to 2nd quadrant

  41. ganeshie8
    • 2 years ago
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    |dw:1381002627185:dw|

  42. ganeshie8
    • 2 years ago
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    |dw:1381002685399:dw|

  43. Study23
    • 2 years ago
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    That makes sense!

  44. Study23
    • 2 years ago
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    Thank you so much for your help! I understand this now!

  45. ganeshie8
    • 2 years ago
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    np :)

  46. Study23
    • 2 years ago
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    :)

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