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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