A car travels 22 km due south and then 28 km in a direction 60° east of south. Find the Direction of the car's resultant Remember that any can be written as a coordinate like this: (AcosΘ,AsinΘ) where A is the magnitude of the object and Θ is the directional angle. So for the car travelling 20km north, that vector can be written as:
(20cos90°, 20sin90°)
Then when the car drives northwest at 60 degrees, that vector can be written as:
(35cos150°, 35sin150°) (do you see why I it's 150°?)
Then, simply calculate each of these coordinates, add them up, and then that resulting coordinate is the coordinate of the resulting displacement vector.
(20cos90°, 20sin90°) = (0, 20)
(35cos150°, 35sin150°) = (-30.31, 17.50)
Displacement vector (x, y) = (-30.31, 37.50)
With this, we can calculate the magnitude which is \displaystyle \sqrt{x^2+y^2}
