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Help me with vectors and magnitudes, please?

  1. Sep 16, 2008 #1
    1. The problem statement, all variables and given/known data
    Vector [tex]\vec{A}[/tex] has magnitude 3.6 units; vector[tex]\vec{B}[/tex] has magnitude 5.9 units. The angle between A and B is 45°. What is the magnitude of [tex]\vec{A}[/tex] + [tex]\vec{B}[/tex]?

    2. Relevant equations
    [tex]\Delta[/tex]V= [tex]\sqrt{V^2x +V^2y}[/tex]
    "SohCahToa"


    3. The attempt at a solution

    I am really struggling with this for some reason. I know its just a SAS triangle.

    Sin(45)=x/5.9 = opposite angle (y component, no?) =4.1719.

    I tried using sqrt(4.1719^2 + 3.6^2)
    where 3.6 is the x component and 4.1719 is the y component
    =5.510

    But, this is not correct. Basically all of my webassign problems are similar to this type, more or less complicated. Could you please point me in the right direction?


    Thank you so very much for your time!
    Edit: I searched but was unable to find a thread that helped. If you know of one, that would be appreciated also
     
  2. jcsd
  3. Sep 16, 2008 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Mathematically, that statement is nonsense.
    What you mean is, if x is the y-component of B, then
    sin(45) = x / 5.9
    so
    x = 5.9 sin(45) = 4.1719
    Let's call it By instead.

    Similarly, what is the x-component Bx of B?

    Then do the vector addition:
    (A + B) = [ Ax + Bx, Ay + By ]
    and then calculate the magnitude using the formula you gave.
     
  4. Sep 17, 2008 #3
    Thank you for the reply!
    Ok, I now understand that I need to calculate the x and y components of each vector.

    By=4.1719
    Bx=[sin(45)=3.6/x]=2.5456

    Ay=[sin(45)=x/3.6]=2.5456
    A=[cos(45)=x/3.6]=2.5456

    Therefore A=5.09117, B=6.7175

    However, when I plug this into the equation I get an incorrect answer (8.4288).


    Can you make it a little more clear? Thank you so much for the help.
     
  5. Sep 17, 2008 #4
    Ok, making progress here.


    I split each of the two vectors up as right triangles with HypA=3.6, HypB=5.9

    Ax will =Ay
    and Bx will = By, because they are 45/45/90 triangles.

    Ay+Ax=5.0912
    By+Bx=8.3486

    But those two numbers do not yield the correct answer in the formula either (9.774473).

    What am I doing wrong? I have gotten other answers on my hw correct.

    Do I need to use the formula twice? Ie (ax, ay), and then (bx, by) then add? Just thinking out loud
     
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