Vector A→, having magnitude 2.5m, pointing 37∘ south of east and vector B→ having magnitude 3.5m, pointing 20∘ north of east are added. What

Question

Vector A→, having magnitude 2.5m, pointing 37∘ south of east and vector B→ having magnitude 3.5m, pointing 20∘ north of east are added. What is the magnitude of the resultant vector?

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Thái Dương 3 years 2021-07-28T00:57:46+00:00 1 Answers 706 views -1

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    -2
    2021-07-28T00:58:53+00:00

    Answer:

    Magnitude of the resultant vector is R = 6.81 m

    Explanation:

    Given :

    Vector A having magnitude of 2.5 m

    Vector A having direction 37 degree south of east.

    Vector B having magnitude of 3.5 m

    Vector B having direction 20 degree north of east.

    Therefore, the angle between the two vectors is, θ = 37+20 = 57 degree

    So, the resultant of the two vectors are given by

    $ R = \sqrt{A^2+B^2+2AB \cos \theta}$

    $ R = \sqrt{2.5^2+3.5^2+2(2.5)(3.5) \cos 57}$

    $ R = \sqrt{6.25+12.25+17.5 \times 0.54}$

    $ R = \sqrt{46.45}$

    R = 6.81 m

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