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Study23 Group Title

Vector Construction help! I've been stuck on this for some time, not sure what to do! Construct c = a + b by drawing and calculating the direction and magnitude of c. The direction should be measured from the +axis. // See illustration below.

  • 10 months ago
  • 10 months ago

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  1. Study23 Group Title
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    |dw:1381002960366:dw|

    • 10 months ago
  2. dav21 Group Title
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    to add 2 vectors you need to connect them tip to end

    • 10 months ago
  3. Study23 Group Title
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    Okay, I got that part but was confused where to go from there

    • 10 months ago
  4. dav21 Group Title
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    |dw:1381003142681:dw|

    • 10 months ago
  5. Study23 Group Title
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    Where do I go from there????

    • 10 months ago
  6. ganeshie8 Group Title
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    drawing part of the question is over, next calculate mag and direction of a+b

    • 10 months ago
  7. Study23 Group Title
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    That's the part where I'm stuck!

    • 10 months ago
  8. Study23 Group Title
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    The mag would be found using pythagorean theorem right?

    • 10 months ago
  9. ganeshie8 Group Title
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    to add vectors, u need to break them into components

    • 10 months ago
  10. dav21 Group Title
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    add the components bro

    • 10 months ago
  11. Study23 Group Title
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    ?

    • 10 months ago
  12. dav21 Group Title
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    break vector into x component and y components then add x components and add y components

    • 10 months ago
  13. ganeshie8 Group Title
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    |dw:1381003391274:dw|

    • 10 months ago
  14. ganeshie8 Group Title
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    |dw:1381003459892:dw|

    • 10 months ago
  15. Study23 Group Title
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    Oh okay! So from there, I would use the pythagorean theorem, and for the direction, I would...?

    • 10 months ago
  16. dav21 Group Title
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    why pythagorean theorem

    • 10 months ago
  17. ganeshie8 Group Title
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    first find the components of a+b

    • 10 months ago
  18. Study23 Group Title
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    for the magnitude

    • 10 months ago
  19. ganeshie8 Group Title
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    x component of a+b = 4.5cos(60) - 8cos(45) y component of a+b = 4.5sin(60) + 8sin(45)

    • 10 months ago
  20. ganeshie8 Group Title
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    ringt ?

    • 10 months ago
  21. ganeshie8 Group Title
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    y components are in same direction, so u add them x components are in opposite directions, so u subtract them

    • 10 months ago
  22. Study23 Group Title
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    How do I know what to subtract from what?

    • 10 months ago
  23. ganeshie8 Group Title
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    number line :)

    • 10 months ago
  24. ganeshie8 Group Title
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    |dw:1381003731661:dw|

    • 10 months ago
  25. ganeshie8 Group Title
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    |dw:1381003758234:dw|

    • 10 months ago
  26. ganeshie8 Group Title
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    we follow that, if ur components are in that direction, they're +ve if they're in opposite, they're -ve

    • 10 months ago
  27. Study23 Group Title
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    Okay!

    • 10 months ago
  28. ganeshie8 Group Title
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    x component of a+b = 4.5cos(60) - 8cos(45) y component of a+b = 4.5sin(60) + 8sin(45)

    • 10 months ago
  29. ganeshie8 Group Title
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    once you have the x and y components for c, to get direction just use the samne formula, \(\theta = \large \tan^{-1} \frac{y}{x}\)

    • 10 months ago
  30. Study23 Group Title
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    what about mag?

    • 10 months ago
  31. ganeshie8 Group Title
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    mag also same formula :- \(\large \sqrt{x^2+y^2}\)

    • 10 months ago
  32. ganeshie8 Group Title
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    a+b is just a vector, so u can use same formulas

    • 10 months ago
  33. Study23 Group Title
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    That makes as a lot more sense, thank you so much!

    • 10 months ago
  34. Study23 Group Title
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    (again!)

    • 10 months ago
  35. ganeshie8 Group Title
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    np :D

    • 10 months ago
  36. Study23 Group Title
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    @ganeshie8 I get 25 degrees for angle?

    • 10 months ago
  37. Study23 Group Title
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    @ganeshie8 ?

    • 10 months ago
  38. ganeshie8 Group Title
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    looks wrong

    • 10 months ago
  39. ganeshie8 Group Title
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    |dw:1381004400621:dw|

    • 10 months ago
  40. ganeshie8 Group Title
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    check ur calculation again :)

    • 10 months ago
  41. ganeshie8 Group Title
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    wolfram says below :- http://www.wolframalpha.com/input/?i=arctan%28%284.5sin%2860%29+%2B+8sin%2845%29%29%2F+%284.5cos%2860%29+-+8cos%2845%29%29%29 add 180 to it, to get into 2nd quadrant maybe

    • 10 months ago
  42. Study23 Group Title
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    ok

    • 10 months ago
  43. Study23 Group Title
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    @ganeshie8 What about if the vectors are being substracted then what do you do with the components for a and b? Is it the same like: we follow that, if ur components are in that direction, they're +ve if they're in opposite, they're -ve

    • 10 months ago
  44. Study23 Group Title
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    The magnitudes is what I'm having trouble with. When I use the formula, I get a decimal answer?

    • 10 months ago
  45. ganeshie8 Group Title
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    yup !

    • 10 months ago
  46. ganeshie8 Group Title
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    for mag just take sqrt(x^2+y^2)

    • 10 months ago
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