Module 2—Motion in Two Dimensions
Lesson Summary
In this lesson you explored the following essential questions:
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How do you mathematically determine the magnitude and direction of the sum of two vectors, such as air velocity and wind velocity, for a flying plane?
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How do you calculate the components of the two vectors to be added when given the magnitudes and directions?
How do you determine the magnitude and direction of the sum of two vectors?
If two vectors 
and 
are given in terms of magnitude and direction, a resultant can be calculated by doing the following:
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Use a vector diagram and trigonometric functions to convert the vectors to component form.
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Add the components (xtotal = x1 + x2) and (ytotal = y1 + y2). Remember to include positive or negative directions.
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Draw the resultant vector using the xtotal component and the ytotal component. Remember to include positive or negative directions.
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Calculate the resultant magnitude using the Pythagorean theorem, c2 = a2 + b2.
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Calculate the direction using the appropriate trigonometric function (tangent function).
Lesson Glossary
vector diagram: a diagram using vectors to show motion
Vector diagrams may instead be used to show forces, fields, or momentum.