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Searching for ## Velocity Vectors

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Physics

You will observe how the motion of an object is determined by head-to-tail vector addition and frames of reference.

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

- Resolve two-dimensional vectors into their components both graphically and quantitatively.
- Use resultant vectors to solve problems involving force and motion both graphically and quantitatively.
- Describe how the motion of an object is determined by its position, velocity, and acceleration.
- Define the head-to-tail method as a means to graphically add vectors together to determine the resultant vector.
- Explain how frames of reference affect the motion of an object.

Vectors represent many physical quantities, like displacement, velocity, electric fields, and more. A vector represents both the magnitude and direction in which the quantity is acting. For velocity, the vector's magnitude tells us the speed in which the object is moving, and its direction of motion is indicated by the arrowhead. When a force acts on an object, it affects its motion. Force is also a vector quantity. To determine the effect of that force on the object, we must analyze the two vectors and determine the resultant vector. There are two methods shown in this Activity Object that use vector addition to determine the resultant vector: the Pythagorean Theorem method and the head-to-tail method. Other methods of vector addition exist, like the parallelogram rule and geometric or trigonometric analysis. However, the two aforementioned methods are the simplest and easiest to understand at an introductory level.

The Pythagorean Theorem in mathematics says that the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side. Thus, we can calculate the quantitative value of the resultant vector using this method. The head-to-tail method of vector addition is a qualitative method for determining the resultant vector. To use this method, the head of one vector is attached to the tail of the other. We then can determine the resultant vector by drawing a third vector to connect the other two vectors. When the head-to-tail method of vector addition is used, the arrowhead of the resultant vector always points toward the arrowhead of the other vectors. Once the three vectors are drawn in position, a triangular vector diagram results.

Inertial frames of references are different observation points from which a motion can be analyzed. In this Activity Object, the inertial frame of reference observes the motion of the ship from overhead, looking down on the ship from the sky. From this observation point, the ship's velocity and the velocity of the ocean's current are seen. The resultant vector is also easily determined from this inertial frame of reference. We could watch the motion of the ship from sea level or other frames of reference, so each observed motion could be slightly different. This is called the relative motion of the ship. Relative motion describes the motion of an object from an observation point. If the observation point changes, how we see the motion changes, and thus the relative motion of the object changes.

Approximate Time | 20 Minutes |

Pre-requisite Concepts | There are no specific pre-requisite concepts necessary. |

Course | Physics |

Type of Tutorial | Concept Development |

Key Vocabulary | direction, head-to-tail method, inertial frame of reference |