Resultant Force?

a force F1 of 35 newtons pulls at an angle of 15 degrees notrth of due east. A force F2 of 75 newtons pulls at an angle of 55 degrees west of due south. Find the magntiude and direction of the resultant force.

Please help me - I have no idea what to do or even where to start!

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asked by Tabby
  1. probably easier for you to do this on x, y axis system

    First find x and y components of first force (15deg above x axis)
    F1x = 35 cos 15
    F1y = 35 sin 15

    now the second force(90-55) = 35 below -x axis)
    F2x = -75 cos 35
    F2y = -75 sin 35
    now add components
    Fx = 35 cos 15 -75 cos 35 = -27.6
    Fy = 35 sin 15 -75 sin 35 = -34.0

    F^2 = Fx^2+Fy^2
    so F = 43.7 in magnitude
    tan theta = Fy/Fx = -43/-27.6
    in quadrant 3 because both are negative
    so theta = 57.3 deg below -x axis
    or 57.3 deg south of west
    or 90-57.3 = 32.7 deg west of south

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    posted by Damon
  2. Ah, thank you so much! You're a lifesaver! Thank you and God bless you for taking the time to help!

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