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?

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mwmovr40 | College Teacher | (Level 1) Associate Educator

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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.