Contextualization

The world around us is full of vectors. Movements, forces, speeds, among many other concepts in Physics, are expressed through these mathematical entities. They allow us to quantify not only the magnitude, but also the direction and sense of a certain phenomenon or property.

A crucial aspect that we will explore in this project is vector decomposition. Vector decomposition is a technique that allows us to divide a vector into two or more parts, called components, which added together, result in the original vector. This ability is extremely useful, since many physical problems involve situations where vectors operate in more than one dimension.

The importance of vector decomposition transcends the classroom and has practical applications in areas as diverse as engineering, meteorology, and even video game animation! For example, civil engineers use vector decomposition to understand the forces acting on a structure and ensure that it is safe and stable. In meteorology, vector decomposition helps predict wind direction and speed. And in video game animation, vector decomposition is used to create realistic movements for characters.

Knowing this, you may wonder: How can I learn more about vectors and their decomposition? Here are some resources to help you understand this topic:

1. Khan Academy: Vector Decomposition https://www.khanacademy.org/math/precalculus/vectors-precalc
2. Song "Vector - Physics with Programming Language" https://www.youtube.com/watch?v=PZ7pkX4FJQI
3. UOL Education: Vectors on the Plane and in Space https://educacao.uol.com.br/disciplinas/fisica/vetores-no-plano-e-no-espaco.htm

It is important to remember that this project goes beyond conceptual understanding and seeks to develop socio-emotional skills, such as time management, communication, problem solving, and creative thinking. So, be prepared to enter the fascinating world of vectors!

Practical Activity

Title: Vector Decomposition in Practice

Project Goal

To learn and apply the theory of vector decomposition through a practical and collaborative activity.

Detailed Project Description

The groups will simulate the launching of objects at different angles to understand how vectors can be decomposed into perpendicular components.

Materials Needed

• Small balls, which can be ping-pong balls, styrofoam or other similar material.
• A measuring tape or tape measure.
• Graph paper.
• Pencil, eraser, ruler, and calculator.

Detailed Step by Step

1. Form groups of 3 to 5 people.
2. Choose a flat and open place to carry out the activity.
3. Use an object to mark the origin point (O) of the launch on the ground.
4. Each group must launch the ball at three different angles - 30º, 45º, and 60º, respectively.
5. The launches must be made so that the ball hits the ground within the test area.
6. After each launch, measure the horizontal (d_x) and vertical (d_y) distances reached by the ball from the origin point.
7. Repeat this procedure three times for each angle.
8. With the data collected, each group should calculate the average of the distances for the horizontal and vertical components of the vectors corresponding to each angle.
9. Finally, represent the vectors on the graph paper using appropriate scales. Remember that the vectors should start at the origin point and their components should be represented by perpendicular lines.

Project Deliverables

At the end of the project, each group will submit a report containing the following topics:

1. Introduction: Contextualization of the theme, its relevance, and application in the real world, as well as the project objective.

2. Development:

   • Theory: Explanation of the theory of vector decomposition.
   • Activity: Detailed description of the activity carried out.
   • Methodology: Explanation of the methodology used for launching the objects, collecting the data, and performing the calculations.
   • Results: Presentation and discussion of the results obtained. Include tables with the data collected and the calculated averages, and graphs of the vectors and their components.

3. Conclusion: Review of the main points, explanation of the learning outcomes, and conclusions drawn about the project.

4. Bibliography: Indication of the sources used to work on the project.

The project should be completed within a month, and each student should dedicate between five and ten hours to its execution.