Physics

A force F 1 of magnitude 5.90 units acts on an object at the origin in a direction θ = 28.0° above the positive x-axis. (See the figure below.) A second force F 2 of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction of the resultant force F 1 + F 2.
magnitude___________? units
direction __________? counterclockwise from the +x-axis

(I tried doing 5.9xcos(28)=5.21N and 5.9xcos(28)+5=10.2N. When I divided them the answers that I got were 11.45 and 63 degrees and they were incorrect I think that I set the problem up incorrectly.

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  1. The angle between two vectors (F₁ and F₂) is 90-28=62°
    The second angle of the force parallelogram is (360 -2•62)/2= 118°.
    Cosine law gives
    F=sqrt (F₁² +F₂² -F₁•F₂•cos118°)= 9.2
    tan α = (5+5.9•sin28°)/5.9•cos28° =1.49
    α = 56.2°

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  2. Fr = 5.9[28o] + 5[90o].

    X = 5.9*Cos28 = 5.2Units.
    Y = 5*sin28 + 5*sin90 = 7.35 Units.

    Fr = sqrt(x^2+y^2) =

    Tan A = Y/X = 7.35/5.2 = 1.41346,
    A = 54.7o = The direction.

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