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How to Calculate Velocity Based on Heading

Calculating velocity based on heading can be useful for navigation in a car or boat, or while walking. It can also be useful for understanding how other objects are traveling, especially in physics applications. Heading, or the direction a body in motion is moving relative to a fixed reference direction, can assist in the calculation of component velocities when a net directional velocity is known. In most cases, heading is considered relative to north, or 0 degrees on a 360-degree compass circle. A simple calculation for speed is the division of distance by time. Velocity is the vector measurement of speed, where direction is also indicated.

Things You'll Need

  • Pen
  • Paper
  • Calculator
  • Protractor
  • Compass
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Instructions

    • 1

      Determine the heading of the object in question. The heading may be measured with a compass or protractor.

    • 2

      Draw a diagram on paper such that the object is at the center of the compass and a vector representing its speed is emanating from it in the heading indicated.

    • 3

      Create a right triangle with the heading and velocity information to set up the calculation of component velocities. The net directional velocity becomes the hypotenuse of the right triangle, with the unknown component velocities represented by the two sides. The right angle of the triangle must be positioned so that one of the sides is parallel to 0 degrees and the other 90 degrees. This is the triangle formed when a perpendicular is dropped from the end of the net velocity vector to a line at 0 degrees.

    • 4

      Calculate the component velocities using trigonometric functions. For one leg, set up an equation to solve for the unknown velocity:

      cos(heading) = (unknown velocity adjacent to heading angle)/(net velocity).

      For the other leg, replace the cosine with the sine function:

      sin(heading)=(unknown velocity opposite heading angle)/(net velocity).

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