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Mechanics AS (Vectors)

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When Studying Vectors, How Would I Go About Answering This Question?

In Each of the following Cases, find the magnitude and direction of the resultant vectors of the two given vectors:

a) a displacement of magnitude 26km on a bearing of 175 degrees and a displacement of magnitude 18km on a bearing 294 degrees

b) Forces of 355 N on a bearing of 320 degrees and 270 N on a bearing of 025 degrees

help would be MUCH appreciated, if you could also explain how you answer it ?

also if you feel like drawing a diagram on paint or something if you could link it?

THANKS :D

  • Mechanics AS (Vectors) -

    in order to add vectors, it's necessary to convert to (x,y) from (r,θ)

    For problem (a), we want to add

    (26,175°) and (18,294°)
    Now, bearings use 0° as North, measured clockwise, so we have to use

    x = r*sinθ
    y = r*cosθ

    (26,175°) -> (2.266,-25.901)
    (18,294°) -> (-16.444,7.321)
    add 'em up to get
    (-14.178,-18.580)
    convert back to (r,θ) to get distance and bearing.

    now go and do (b) the same way

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