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A very strong girl runs 200 miles east for several hours. After a brief rest she runs another 100 miles north. She stops for the night at a local bed and breakfast and the next morning walks 75 miles directly south-east. Find the magnitude and direction of her displacement.

  • resultant vector -

    I can do that in weeks or months, not hours!

    Total displacement is the sum of the components of individual displacements. Most of the time, displacements are resolved in x (or east) and y (north) directions.

    200 miles -> east = (200,0)
    100 miles -> north = (0,100)
    75 miles -> S/E = (75√(1/2),-75√(1/2))
    Add up the three vectors to get:
    (253,147), i.e.
    253 miles towards east, 147 towards north.
    Alternatively, it can be combined to form a single vector (use Pythagoras theorem):
    257.4 miles in the direction NθE where θ=arctan(253/147)=59.8° approx.

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