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anonymous

  • 3 years ago

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.

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  1. anonymous
    • 3 years ago
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    |dw:1381002960366:dw|

  2. anonymous
    • 3 years ago
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    to add 2 vectors you need to connect them tip to end

  3. anonymous
    • 3 years ago
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    Okay, I got that part but was confused where to go from there

  4. anonymous
    • 3 years ago
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    |dw:1381003142681:dw|

  5. anonymous
    • 3 years ago
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    Where do I go from there????

  6. ganeshie8
    • 3 years ago
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    drawing part of the question is over, next calculate mag and direction of a+b

  7. anonymous
    • 3 years ago
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    That's the part where I'm stuck!

  8. anonymous
    • 3 years ago
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    The mag would be found using pythagorean theorem right?

  9. ganeshie8
    • 3 years ago
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    to add vectors, u need to break them into components

  10. anonymous
    • 3 years ago
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    add the components bro

  11. anonymous
    • 3 years ago
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    ?

  12. anonymous
    • 3 years ago
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    break vector into x component and y components then add x components and add y components

  13. ganeshie8
    • 3 years ago
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    |dw:1381003391274:dw|

  14. ganeshie8
    • 3 years ago
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    |dw:1381003459892:dw|

  15. anonymous
    • 3 years ago
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    Oh okay! So from there, I would use the pythagorean theorem, and for the direction, I would...?

  16. anonymous
    • 3 years ago
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    why pythagorean theorem

  17. ganeshie8
    • 3 years ago
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    first find the components of a+b

  18. anonymous
    • 3 years ago
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    for the magnitude

  19. ganeshie8
    • 3 years ago
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    x component of a+b = 4.5cos(60) - 8cos(45) y component of a+b = 4.5sin(60) + 8sin(45)

  20. ganeshie8
    • 3 years ago
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    ringt ?

  21. ganeshie8
    • 3 years ago
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    y components are in same direction, so u add them x components are in opposite directions, so u subtract them

  22. anonymous
    • 3 years ago
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    How do I know what to subtract from what?

  23. ganeshie8
    • 3 years ago
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    number line :)

  24. ganeshie8
    • 3 years ago
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    |dw:1381003731661:dw|

  25. ganeshie8
    • 3 years ago
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    |dw:1381003758234:dw|

  26. ganeshie8
    • 3 years ago
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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

  27. anonymous
    • 3 years ago
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    Okay!

  28. ganeshie8
    • 3 years ago
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    x component of a+b = 4.5cos(60) - 8cos(45) y component of a+b = 4.5sin(60) + 8sin(45)

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

  30. anonymous
    • 3 years ago
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    what about mag?

  31. ganeshie8
    • 3 years ago
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    mag also same formula :- \(\large \sqrt{x^2+y^2}\)

  32. ganeshie8
    • 3 years ago
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    a+b is just a vector, so u can use same formulas

  33. anonymous
    • 3 years ago
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    That makes as a lot more sense, thank you so much!

  34. anonymous
    • 3 years ago
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    (again!)

  35. ganeshie8
    • 3 years ago
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    np :D

  36. anonymous
    • 3 years ago
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    @ganeshie8 I get 25 degrees for angle?

  37. anonymous
    • 3 years ago
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    @ganeshie8 ?

  38. ganeshie8
    • 3 years ago
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    looks wrong

  39. ganeshie8
    • 3 years ago
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    |dw:1381004400621:dw|

  40. ganeshie8
    • 3 years ago
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    check ur calculation again :)

  41. ganeshie8
    • 3 years ago
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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

  42. anonymous
    • 3 years ago
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    ok

  43. anonymous
    • 3 years ago
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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

  44. anonymous
    • 3 years ago
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    The magnitudes is what I'm having trouble with. When I use the formula, I get a decimal answer?

  45. ganeshie8
    • 3 years ago
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    yup !

  46. ganeshie8
    • 3 years ago
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    for mag just take sqrt(x^2+y^2)

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