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An airplane flies 200 km due west from city A to City B and them 300 km in the direction of 30.0 degrees north of west from city B to city C. In straight-line distance, how far is city C from city A? Relative to city A, in what direction is city C?

  • Physics -

    Calculate the cumulative coordinates of B and C relative to A by resolving the distances into X(east) and Y(north) components.
    From A to B, distance Db = 200 km,
    direction = 180 degrees.
    x=Db.cos(180)=-200
    y=Db.sin(180)=0
    Therefore the coordinates of B relative to A are (-200,0).

    From B to C:
    Distance Dc = 300 km
    direction = 180-30=150 degrees.
    x=300 cos(150)=-259.81 km
    y=300 sin(150)=150 km
    The coordinates of C relative to B are (-259.81, 150).

    The cumulative coordinate relative to A are
    (-200+(-259.81), 0+150)
    =(-459.81, 150)

    Can you now calculate the distance and direction?

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