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24 January, 19:31

Compute the magnitude and direction of the sum of the two vectors: 170N of force at 87° and 100N of force at 46°.

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  1. 24 January, 19:51
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    F = 254.08N Θ = 72.03°

    Step-by-step explanation:

    First of all we find the resolution in both x and y axis

    ∑Fx = 170cos87 + 100cos46 = 78.36N

    ∑Fy = 170sin87 + 100sin46 = 241.70N

    To find the resultant vector we use pythagorean theorem

    F = √ (∑Fx) ² + ∑ (Fy) ²

    F = √ (78.36² + 241.70²)

    F = √ (64559.1796)

    F = 254.08N

    the angle between both force can be obtained using

    tanθ = ∑Fy / ∑Fx

    tanθ = 241.70 / 78.36

    tanθ = 3.084

    Θ = tan⁻ 3.084

    Θ = 72.03°
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