Context
Physics is a fundamental science that helps us understand the world around us. It explains everything from the simplest movements we make, like walking and throwing a ball, to the most complex phenomena in the universe, such as the movement of planets and the expansion of the Universe. In our daily lives, we use Physics concepts even without realizing it. And one of these concepts is vectors.
Vectors are mathematical entities that have both magnitude (size) and direction. They are essential for describing a wide range of physical phenomena, from forces to velocities and accelerations. One of the most important skills when working with vectors is the ability to decompose a vector into components. This skill allows solving complex Physics problems in a simpler way.
Decomposing a vector means breaking it down into smaller parts that, when added together, result in the original vector. A common way to do this is by dividing the vector into components that are perpendicular to each other. For example, we can decompose a force vector into its horizontal and vertical components. This skill is fundamental for solving a wide range of problems, from oblique launches to force equilibrium.
Understanding vector decomposition is crucial to grasp various areas of Physics, such as Mechanics, Electromagnetism, and Quantum Physics. This not only allows solving practical problems but also understanding more abstract and complex concepts. For example, in Quantum Mechanics, vectors are used to describe the state of subatomic particles.
This project focuses on the study of vectors and their decomposition. This knowledge is essential for understanding various areas of Physics and even other sciences like Engineering and Computer Science. Beyond the academic scope, the ability to think in terms of components and directions has useful applications. For example, in playing video games involving movement in two or three dimensions, or in maritime and aerial navigation.
Recommended resources for studying the topic:
- Halliday, D., Resnick, R., Walker, J.: "Fundamentals of Physics. Volume 1: Mechanics". LTC, Rio de Janeiro, 8th ed., 2009. (The book addresses the topic of vectors and their decomposition in Chapter 3.)
- Site Brasil Escola – Vectors: https://brasilescola.uol.com.br/matematica/vetores.htm (The page offers various texts and exercises on vectors.)
- Khan Academy – Vectors: https://pt.khanacademy.org/math/precalculus/vectors-precalc (The platform features various videos and exercises for practicing the content.)
- YouTube – Channel Ciência Todo Dia: https://www.youtube.com/cienciatododia/ (The channel has several didactic videos that address Physics concepts, including vectors.)
Practical Activity
Activity Title: Vector Browser Project
Project Objective:
Explore vector decomposition through the creation of a simple navigation game. For this, students should integrate knowledge of Physics and Computer Science, developing technical and socio-emotional skills.
Detailed Project Description:
Students should create a simple computer navigation game, where the player must move an object on a 2D grid. The direction and magnitude of movements should be controlled by vectors, which must be decomposed into their x and y components during the game programming. The game should also include obstacles that the player must avoid, thus increasing the complexity of the problem and the need for a good understanding of vector decomposition.
Required Materials:
- Computers with internet access.
- Free account on the p5.js programming platform p5.js Web Editor.
Step-by-Step Guide for the Activity:
- Theoretical Study: Students should review the theory of vectors and their decomposition.
- Planning: In groups, they should outline a plan for the game creation. This plan should include the grid layout, game rules, and programming strategy for object movement.
- Programming: Students should use the p5.js platform to program the game according to the plan. They should create vectors for object movement and decompose these vectors into their x and y components.
- Testing and Adjustments: After the initial programming, students should test the game and make necessary adjustments.
- Presentation and Report: Finally, students should prepare a game presentation for the classroom and write a detailed report on the project.
Project Deliverables:
- Written Report: The report should follow the suggested format with an introduction (including the context of the theme, its relevance, and the project objective description), development (with the theory of vectors and their decomposition, detailed activity description, methodology used, and results obtained), and conclusion (with the learnings and final considerations on the project). Additionally, it should include the bibliography used.
- Presentation: The presentation should include a game demo and an explanation of how vector decomposition was used in the project.
- Source Code: The game source code should be delivered through the p5.js platform. It should be well-commented, explaining the functions and logic used.
These activities aim not only to assess students' knowledge in the theory of vectors and their decomposition but also their teamwork, creativity, problem-solving, and time management skills. It is important for them to understand that the written part is as important as the practical part of the project, as one complements the other. In the report, they should not only describe what they did but also justify their choices and explain the difficulties encountered and how they overcame them.
