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Component Addition (i.e., Analytical Method of Vector Addition)

Vectors - Motion and Forces in Two Dimensions - Lesson 1 - Vectors: ... For instance, two displacement vectors with magnitude and direction of 11 km, North and ... to use the Pythagorean theorem to determine the resultant for the addition of three ... Theta (Θ) can be calculated using one of the three trigonometric functions ...

For more information, see Component Addition (i.e., Analytical Method of Vector Addition)


Required key points

  • The object's total displacement is equal to the sum of its vectors. Adding the components is another approach to add vectors.
  • A resultant vector is obtained by adding or subtracting any number of vectors.
  • Arrange the two components so that component tail begins at the head of the previous vector component. 

Step 1: In a coordinate system, displaying the resultant vector and components.

Total displacement = 27 m

Angle between the horizontal and resultant \theta = 30 \degree

Step 2: Using the trigonometric ratios to find the magnitude of the vertical displacement.

\sin \theta = \frac{\text{ vertical component }}{27 m}

\text{ vertical component } = 27 * sin 30\degree = 27 * \frac{1}{2}

\text{ vertical component } = 13.5

The vertical component is directed downward and must have a negative value.

\text{ vertical component } = - 13.5