calculus

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three forces with magnitudes 100, 50, and 80 lb act on an object at angles of 50 degree, 160 degree, and -20 degree respectively. ind the direction and magnitude o the resultant force.

  • calculus -

    express each as a vector in component form

    magnitude 100,direction 50
    = (100cos50, 100sin50) = (64.279 , 76.604)
    mag50,direction160
    = (-8.682 , 17.101
    mag80, direction -20
    = ( 75.175 , -27.361)

    add up the 3 vectors
    = (130.772 , 66.344)

    magnitude = √(x^2 + y^2) = 146.638
    direction :
    tan Ø = 66.344/130.772
    Ø = 26.9° or 333.1°
    but my sketch showed the resultant to be in the first quadrant, so
    Ø = 26.9°

  • calculus -

    mag50,direction160 = (-46.985,17.101)

  • calculus -

    you messed up mag50, direction160
    =(-46.984, 17.101

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