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Magnitude of displacement

  1. Dec 11, 2011 #1
    1. The problem statement, all variables and given/known data
    1.jpg
    Compute the magnitude of the displacement ([itex]\vec{}R[/itex] and the angle with respect to the x-axis.


    2. Relevant equations



    3. The attempt at a solution

    A = 10m * sin30° [itex]\hat{}y[/itex]+ 10m * cos30° [itex]\hat{}x[/itex]

    [itex]\vec{}A[/itex] = 5m [itex]\hat{}y[/itex] + 8.66m [itex]\hat{}x[/itex]

    B = 15m

    C = 20m * sin80° [itex]\hat{}x[/itex] + 20m * cos80° [itex]\hat{}y[/itex]

    [itex]\vec{}R[/itex] = [itex]\hat{}A[/itex] + [itex]\hat{}B[/itex] + [itex]\hat{}C[/itex]
    [itex]\hat{}R[/itex] = √(43.36m)2 + (1.58m)2 = 64.34m

    tanθ = 43.36/1.58
    = 87°

    Is this correct? Please help!
     
  2. jcsd
  3. Dec 11, 2011 #2

    NascentOxygen

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    Staff: Mentor

    Your breakdown of Vector C isn't quite right.
     
  4. Dec 11, 2011 #3
    Thanks.. Would it just be 20m * cos80° in the y-direction and none in the x-dir?
     
  5. Dec 11, 2011 #4

    NascentOxygen

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    Staff: Mentor

    No, not if that's 80 degrees to the horizontal. Unless a vector lies exactly along the x (or y) axis, it must resolve into both x and y components.
     
  6. Dec 11, 2011 #5
    I noticed I'm missing a negative in the y direction, but how will I correctly break it into its components? I can make a triangle from the dotted line to the bottom arrow of C, but I'm not so sure of what to use.
     
  7. Dec 11, 2011 #6

    NascentOxygen

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    Staff: Mentor

    To make it easier to visualize, in your rough working (which only you see) draw the angle so that it's more like 70 degrees than 80 so you have more space on the paper to work with. Then construct that triangle you spoke of, and determine the lengths of its vert and horiz sides.

    There is more amiss than the missing - sign.
     
  8. Dec 11, 2011 #7
    draw the triangle on the inside of the picture? I am so losttt :cry:
     
  9. Dec 11, 2011 #8

    NascentOxygen

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    Staff: Mentor

    Vector C is almost vertical, so when you break it into its components, the longest of these components is going to be the vertical one. Check that you have this correct.
     
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