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Babynini

  • one year ago

Magnitudes and directions of vectors.

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  1. Babynini
    • one year ago
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    The magnitudes and directions of two forces acting at a point p are given. Approximate the magnitude and direction of the resultant vector, accurate to two decimal places a) 5.00lb, 200 degrees b) 7.00lb, 65 degrees.

  2. Babynini
    • one year ago
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    @jim_thompson5910 :P can we do this one?

  3. jim_thompson5910
    • one year ago
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    |dw:1433465574025:dw|

  4. jim_thompson5910
    • one year ago
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    |dw:1433465584644:dw|

  5. jim_thompson5910
    • one year ago
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    |dw:1433465617485:dw|

  6. jim_thompson5910
    • one year ago
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    |dw:1433465663391:dw|

  7. jim_thompson5910
    • one year ago
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    find the component <x,y> form of each vector then you can add up the vectors component-wise

  8. jim_thompson5910
    • one year ago
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    x = r*cos(theta) y = r*sin(theta)

  9. Babynini
    • one year ago
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    Where do I derive the r from?

  10. jim_thompson5910
    • one year ago
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    r = distance from origin to vector tip r = magnitude of vector (ie force applied)

  11. Babynini
    • one year ago
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    so 5 for part a a) would be 5cos(200) 5sin(200) ?

  12. jim_thompson5910
    • one year ago
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    yes

  13. Babynini
    • one year ago
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    a = <-4.698,-1.710>

  14. Babynini
    • one year ago
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    b= <2.958,6.344>

  15. Babynini
    • one year ago
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    and when I add those up I get = <-1.74,4.63>

  16. jim_thompson5910
    • one year ago
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    they want it "accurate to two decimal places"

  17. Babynini
    • one year ago
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    ...that's what I did o.0

  18. Babynini
    • one year ago
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    oh, I didn't do a and b accurate to two decimal places but that's because that's part of the process to get to the final answer and should be more accurate I think (hence more decimal places) but the final answer is ok, yeah?

  19. jim_thompson5910
    • one year ago
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    hmm maybe they just want the final answer to 2 decimal places, the steps just leave it to 15 or so (let the calculator handle it)

  20. Babynini
    • one year ago
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    haha k. final answer looks good though? :)

  21. jim_thompson5910
    • one year ago
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    yes it looks perfect. I'm getting the same

  22. jim_thompson5910
    • one year ago
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    oh wait

  23. jim_thompson5910
    • one year ago
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    they don't want the <x,y> form of the resultant they want the "magnitude and direction of the resultant vector"

  24. Babynini
    • one year ago
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    ou.

  25. jim_thompson5910
    • one year ago
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    r = magnitude theta = direction r = sqrt(x^2 + y^2) theta = arctan(y/x) will give you the angle, but it will say some angle in Q4. Add on 180 degrees to move the angle to Q2 <x,y> = <-1.74,4.63> is in Q2

  26. Babynini
    • one year ago
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    so magnitude: 4.95

  27. jim_thompson5910
    • one year ago
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    yes

  28. jim_thompson5910
    • one year ago
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    |dw:1433466781150:dw|

  29. Babynini
    • one year ago
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    theta = 110.58

  30. jim_thompson5910
    • one year ago
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    nvm, my drawing is way off and not to scale

  31. jim_thompson5910
    • one year ago
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    the "7 lb" vector should be longer, that's probably why

  32. Babynini
    • one year ago
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    It's all good.

  33. jim_thompson5910
    • one year ago
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    I'm getting roughly the same theta

  34. Babynini
    • one year ago
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    haha yeah just a little disproportional xD

  35. Babynini
    • one year ago
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    have you been rounding? I have been using calculator storages

  36. jim_thompson5910
    • one year ago
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    I got 110.581677969387

  37. Babynini
    • one year ago
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    yep yep :) same.

  38. Babynini
    • one year ago
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    So final answer is The magnitude : 4.95 The direction = 110.58

  39. jim_thompson5910
    • one year ago
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    yes

  40. Babynini
    • one year ago
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    Fantastic! I like this question better than the car one heh

  41. jim_thompson5910
    • one year ago
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    yeah much easier

  42. Babynini
    • one year ago
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    For sure

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