Posted by **Brenden** on Sunday, September 20, 2009 at 4:01pm.

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 -
**MathMate**, Sunday, September 20, 2009 at 4:40pm
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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