Contextualization

The study of vectors is essential to understand how objects and entities move in space. This is as true when we are talking about a vehicle moving along a road as it is about a planet orbiting a star. And understanding the 'difference' between vectors, or, in other words, how to subtract one vector from another, is a crucial part of understanding how to direct or orient these movements.

In this project, we will delve deeply into the world of vectors, with a specific focus on vector subtraction. A vector has both magnitude (how 'big' it is, or length) and direction (where it is pointing). When we subtract one vector from another, we are essentially finding a new vector that represents the difference in magnitude and direction between the two original vectors.

The applications of vectors are broad and varied, ranging from Physics, Engineering, Computing, and even Biology and Economics. Whether piloting an airplane, designing a building, programming a video game, or modeling the spread of a disease, we need to understand how things move and interact in space. Therefore, the topic of this project is not only a key theoretical concept for the study of Physics, but it also has real practical applications in everyday life and in many professional careers.

Theoretical Introduction

Let's start with a review of what a vector is. In Physics, a vector is a quantity that has both magnitude and direction. We can represent a vector as an arrow pointing in a certain direction - the length of the arrow represents the magnitude of the vector, and the way the arrow points represents the direction.

Vector subtraction follows a slightly different process from the subtraction of numbers we are used to. Instead of simply subtracting the magnitudes (or lengths) of the vectors, we need to consider both the magnitude and direction of each vector. In simple terms, vector subtraction involves reversing the direction of the vector being subtracted and then adding it to the first vector.

This project will challenge you to apply these theoretical concepts in a series of practical tasks. In this way, you will be able to solidify your understanding of these concepts, as well as develop teamwork, time management, and problem-solving skills.

Practical Activity

Title: Building Vectors: The Discovery of the Difference!

Project Objective:

This project aims to provide students with a clear understanding of vectors and, in particular, vector subtraction. Students will need to apply vector concepts to create physical models, as well as develop a conceptual understanding of how vectors behave and how vector subtraction works. Additionally, we also aim to develop teamwork, time management, effective communication, problem-solving, and critical thinking skills.

Detailed Project Description:

Students will be divided into groups of 3 to 5, where they will need to create a physical model of a real scenario involving the use of vectors. Students will need to create the scenario, identify the vectors involved, their directions and magnitudes, and perform vector subtraction. After completing the practical activity, the groups must make a video of up to 15 minutes explaining the entire activity, what they learned, what difficulties they encountered, and how they solved them. Finally, with the help of this video, the group must prepare a project report containing the sections: Introduction, Development, Conclusions, and Bibliography. The project should last approximately two weeks, with each student dedicating approximately 12 hours to the project.

Required Materials:

• Cardboard
• Barbecue sticks
• Paint or colored markers
• Ruler
• Camera (can be a cellphone camera)
• Computer with internet access

Activity Step-by-Step:

1. Identifying a scenario: Each group must identify and discuss a real-world scenario involving the use of vectors. Examples of scenarios may include the movement of cars on a road, the flight of an airplane, the movement of a boat on a river, etc.

2. Creating the physical model: Based on the chosen scenario, the group must create a physical model using cardboard, barbecue sticks, and markers. This model should represent all the important vectors and clearly show their directions and magnitudes.

3. Subtracting the vectors: The group must demonstrate and document the subtraction of two or more vectors in the chosen scenario. This involves identifying the vectors to be subtracted, reversing the direction of the vector being subtracted, and then adding it to the first vector.

4. Make a video: The group must make a video of up to 15 minutes explaining the scenario, the model, and the process of vector subtraction. The video should clearly show how vector subtraction is performed in the chosen scenario.

5. Preparing the report: Based on the video, the group must prepare a detailed report on the project. This report should follow the structure: Introduction, Development, Conclusions, and Bibliography. In the Introduction, the chosen scenario and the relevance of vectors to it should be explained. In the Development, the process of building the model, how the vectors were subtracted, and what the results were should be detailed. In the Conclusions, what was learned, what challenges were encountered, and how they were overcome should be discussed. In the Bibliography, all sources that assisted in the project development should be cited.

Project Delivery

For the completion of the project, groups must deliver:

1. A video of up to 15 minutes explaining the practical activity;
2. Detailed report containing the sections: Introduction, Development, Conclusions, and Bibliography.

These deliveries allow students to demonstrate not only a theoretical understanding of vector subtraction but also a practical understanding and application of this concept in a real-world scenario. In addition to subject knowledge, students must also demonstrate the socio-emotional skills acquired, such as teamwork, communication, problem-solving, among others, both in the video and in the report discussion.