An airplane flies with a velocity of 750 kilometers per hour, 30 degrees south of east. what is the magnitude of the eastward component of the plane's velocity?
This is an example of a vector problem. Velocity is an example of a property of an object that requires not only a size and a unit, but also must include a direction. Any quantity that needs a direction to complete its description is a vector. Vectors can be represented on a Cartesian coordinate plane in several different ways. One of which is to draw the vector as an arrow which has a length on the coordinate plane that is proportional to the size (magnitude) of the real vector. The direction the arrow points on the plane is defined relative to a reference angle in such a way as to represent the direction of the real vector. Most times the reference is the positive x-axis and the direction of the vector is measured as an angle away from the x-axis (positive if it is a counter-clockwise angle, and negative if it is a clockwise angle).
The vector image on a coordinate plane can be broken into two simple rays that measure the horizontal and vertical distances necessary to be covered to create a right triangle which has a hypotenuse that corresponds to the vector. The horizontal distance is called the horizontal, or X, component of the vector; the vertical distance is called the vertical, or Y, component. To determine the size (magnitude) of the components we simply have to apply the rules of right angle trigonometry:
horizontal comp = Vector x cosine(angle)
vertical comp = Vector x sine(angle).
In the problem, the horizontal component refers to the Easterly direction and the vector is -30 degrees to the reference line. Thus the magnitude (size) of the easterly component will be given by
Eastward componant = 750km x cosine(-30) = 650 km East.