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Searching for ## Velocity Vectors

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Physics

You will find the location of a missing plane by adding and resolving velocity vectors.

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After completing this tutorial, you will be able to complete the following:

- Determine the magnitude of vector components.
- Distinguish between the x- and y-components of a vector.
- Calculate the resultant velocity of parallel vectors by addition or subtraction of the vectors.
- If presented with the sum of the x- and the y-components, calculate the magnitude of the resultant velocity using the Pythagorean theorem.
- Distinguish between the parallelogram and the head-to-tail method of vector addition.

A vector is a quantity that must be specified not only by magnitude but also by direction. Vectors are represented by arrows that point in the direction of the quantity and have a length which represents the vector's magnitude. Vectors may represent acceleration, force, momentum, and velocity.

Vectors can be calculated using simple mathematical procedures. For example, in vector addition, adding two vectors that act along parallel directions is solved by addition if they are acting in the same direction, or if they act in opposite directions, they are subtracted. The process of replacing two or more vectors by one equivalent vector is called finding the resultant.

To find the resultant of vectors that act in different or opposite directions, the parallelogram method or head-to-tail method may be used. : In the parallelogram method, a scale is selected, and the parallel vectors of each vector are accurately drawn. Using the tail of the vector as the origination point, draw one vertical line and one horizontal line. Using the head of the vector as another origination point, draw one horizontal line and one vertical line. The lines that were drawn will meet to form a parallelogram. In the head-to-tail method, where the head of the first vector ends, the tail of the second vector begins. The resultant vector is then accurately drawn to scale from the tail of the first vector to the head of the last vector.

The resultant of two vectors depends not only on the magnitude of the two vectors being added, but also on the angle between the two vectors. To find the magnitude of two perpendicular vectors, apply the Pythagorean theorem. For example, to calculate the magnitude of a pair of 100 km/h velocity vectors that are at right angles to each other, the following mathematical formula would apply:

Approximate Time | 20 Minutes |

Pre-requisite Concepts | Students should be familiar with the definition of a vector and the Pythagorean theorem. |

Course | Physics |

Type of Tutorial | Concept Development |

Key Vocabulary | acceleration, force, ground speed |