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Resultant Vector using Components

  1. Sep 1, 2014 #1
    1. The problem statement, all variables and given/known data

    A man pushing a toy car causes it to undergo 2 displacements. The first has a magnitude of 150 cm and makes an angle of 120degrees with the positive x axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of 35 degrees at the positive x axis. Find the magnitude and direction of the second displacement.



    3. The attempt at a solution


    Displacement A + Displacement B = Displacement R
    B = R - A

    R = Rx + Ry
    R = 140cos35i + 140sin35j

    180° - 120° = 60
    A = Ay + Ax
    A = 150sin60j - 150cos60i (2nd Quad?? Not too sure if need to put negative here)

    Hence:
    B = Rx + Ry - (Ay + Ax)
    B = 140cos35i + 140sin35j - (150sin60j - 150cos60i)
    B = (140cos35 +150cos60)i + (140sin35 - 150sin60)j

    B = sqrt( Bi^2 + Bj^2 )
    B = 196

    To find Direction
    tetha = taninverse( (140sin35 - 150sin60)/ (140cos35 +150cos60) )
    tetha = -14.65 degrees ?? weird??
     
  2. jcsd
  3. Sep 1, 2014 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes. cos(120)= -cos(60). If you are not certain of the sign leave it as cos(120) and sin(120).

    Yes, that is correct.

    What is weird about it? Did you draw a picture?
     
  4. Sep 1, 2014 #3
    Yes i just drew it. So -14.65 means theta is 360 - 14.65? I suck at math
     
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