Objectives (5 - 7 minutes)

1. Introduce the concept of vertical motion and its characteristics, focusing on free fall and uniformly accelerated motion.
2. Develop the ability to solve problems related to vertical motion, applying the formulas and concepts learned.
3. Use practical examples and everyday applications to reinforce understanding of vertical motion.

Secondary Objectives:

• Stimulate active participation of students through questions and discussions.
• Foster critical thinking and problem-solving skills.
• Promote collaboration among students, encouraging them to work in groups to solve the proposed problems.

Introduction (10 - 12 minutes)

1. Review of previous concepts: The teacher starts the lesson by reviewing the concepts of uniform motion and uniformly accelerated motion, which were studied in previous classes. This review is essential for students to understand the new content that will be covered. (3 - 4 minutes)

2. Presentation of problem situations: The teacher proposes two problem situations involving vertical motion. The first one could be: 'Imagine you are in a building and drop a marble. How does it behave as it falls?'. The second one could be: 'A skydiver jumps from a plane. What is his motion during free fall?'. These situations aim to arouse students' curiosity and initiate the discussion on the lesson's topic. (3 - 4 minutes)

3. Contextualization of the subject: The teacher contextualizes the importance of studying vertical motion, explaining that many natural and technological phenomena, such as the fall of an object, the flight of a bird, and the operation of an elevator, can be understood and predicted from this concept. Additionally, the teacher may mention the relevance of the topic for practical applications, such as calculating parachute jumps and building elevators. (2 - 3 minutes)

4. Student engagement: To capture students' attention, the teacher can share curiosities and stories related to vertical motion. For example, they can mention the experience of the scientist Galileo Galilei, who dropped two spheres of different masses from the Leaning Tower of Pisa to prove that they hit the ground at the same time, challenging the common belief of the time. Another curiosity is the existence of a point on Earth called the Pole, where a vertical stick can be balanced due to the centrifugal force caused by the planet's rotation. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Theory of Vertical Motion (10 - 12 minutes)

   1.1. Free Fall: The teacher begins by explaining the concept of free fall, which is the motion of an object under the exclusive influence of gravity. In this type of motion, the only force acting is gravity, and therefore, the object falls with constant acceleration. The teacher can use the example of the marble dropped from the building, mentioned in the Introduction, to illustrate this concept. (3 - 4 minutes)

   1.2. Free Fall Equation: The teacher presents the equation of motion in free fall, which is given by h = (1/2)gt², where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s²), and t is the time. The teacher explains that this equation is valid only when the object is dropped from a great height and air resistance is negligible. (2 - 3 minutes)

   1.3. Fall Time: The teacher explains that the fall time of an object in free fall is given by the formula t = √(2h/g). The teacher can perform a simple demonstration, calculating the fall time of an object dropped from a certain height. (2 - 3 minutes)

   1.4. Velocity in Free Fall: The teacher introduces the concept of velocity in free fall, explaining that the object's velocity continuously increases during the fall due to the constant acceleration of gravity. The equation for velocity in free fall is v = gt, where v is the velocity and t is the time. (2 - 3 minutes)

2. Uniformly Accelerated Motion (10 - 12 minutes)

   2.1. Definition: The teacher presents the concept of uniformly accelerated motion, which is the motion of an object under the action of a constant acceleration that is not gravity. The teacher explains that, in this type of motion, the object's velocity varies uniformly over time. (2 - 3 minutes)

   2.2. Equation of Uniformly Accelerated Motion: The teacher presents the equation of uniformly accelerated motion, which is given by v = v0 + at, where v is the final velocity, v0 is the initial velocity, a is the acceleration, and t is the time. The teacher can use the example of the skydiver in free fall, mentioned in the Introduction, to illustrate this concept. (2 - 3 minutes)

   2.3. Torricelli's Equation: The teacher introduces Torricelli's equation, which is another way to express uniformly accelerated motion. Torricelli's equation is v² = v0² + 2ad, where d is the distance traveled. (2 - 3 minutes)

   2.4. Applications of Uniformly Accelerated Motion: The teacher presents some applications of uniformly accelerated motion, such as calculating the distance traveled by a car on a race track and calculating the final velocity of an elevator. (2 - 3 minutes)

3. Discussion and Problem Solving (5 - 8 minutes)

   3.1. The teacher proposes some hypothetical problems for students to solve in groups. The problems should involve the application of the formulas and concepts presented. For example: 'An astronaut in free fall on the Moon drops an object from a height of 10 meters. How long does it take for the object to reach the ground? And with what velocity does it hit the ground?'. Another example: 'An elevator is descending with an acceleration of 2 m/s². If an object is dropped in the elevator from rest, how long does it take for the object to reach the bottom of the elevator? And with what velocity does it hit the bottom of the elevator?'. (3 - 5 minutes)

   3.2. After students solve the problems, the teacher asks some groups to present their solutions. During the presentations, the teacher asks questions to verify students' understanding and to correct any errors. (2 - 3 minutes)

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes)

   • The teacher should promote a group discussion with all students, where each group shares the solutions found for the problems proposed during the Development of the lesson.
   • During this discussion, the teacher should encourage students to explain how they arrived at their answers, which formulas and concepts they applied, and why.
   • The teacher should also ask questions so that students can reflect on the solutions of other groups, stimulating the exchange of ideas and the development of critical thinking.

2. Connection with Theory (2 - 3 minutes)

   • After the discussion, the teacher makes the connection between the practice carried out and the theory presented.
   • The teacher reinforces the concepts of free fall and uniformly accelerated motion, explaining how these concepts were applied to solve the proposed problems.
   • The teacher also highlights the importance of understanding these concepts for the comprehension of everyday phenomena and for the resolution of practical problems.

3. Individual Reflection (2 - 3 minutes)

   • The teacher proposes that students reflect individually on what they learned during the lesson.
   • The teacher asks some questions to guide students' reflection, such as: 'What was the most important concept learned today?', 'What questions have not been answered yet?' and 'How can you apply what you learned today in situations in your daily life?'.
   • The teacher gives a minute for students to think about these questions and then asks some students to share their answers with the class.
   • This reflection is important so that students can consolidate what they learned and so that the teacher can assess the effectiveness of the lesson.

4. Feedback and Closure (1 minute)

   • Finally, the teacher requests feedback from students about the lesson, asking if they found the content difficult or easy, if the explanations were clear, if the activities were interesting, among others.
   • The teacher thanks the students for their participation, reinforces the importance of continuous study, and gives a brief preview of what will be covered in the next lesson.

Conclusion (5 - 7 minutes)

1. Content Summary (2 - 3 minutes)

   • The teacher recaps the main points covered in the lesson, reinforcing the difference between free fall and uniformly accelerated motion, the equations and formulas used to calculate the time, velocity, and distance in each type of motion, and the practical applications of these concepts.
   • For example, the teacher can review the equation of free fall (h = (1/2)gt²), the equation for fall time (t = √(2h/g)), the equation for velocity in free fall (v = gt), the equation of uniformly accelerated motion (v = v0 + at), and Torricelli's equation (v² = v0² + 2ad).
   • The teacher can also review the practical examples discussed during the lesson, such as the fall of an object dropped from a height and the motion of a skydiver in free fall.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes)

   • The teacher highlights how the lesson connected theory, practice, and applications of vertical motion.
   • The teacher explains that the theory was presented through clear explanations and simple examples, practice was carried out through group problem-solving, and applications were discussed based on everyday phenomena and practical situations.

3. Additional Materials (1 - 2 minutes)

   • The teacher suggests some complementary study materials for students who wish to deepen their knowledge of vertical motion.
   • The materials may include Physics books, educational videos online, virtual experiment websites, among others.
   • For example, the teacher can suggest the book 'Physics for High School' by Antônio Máximo and Beatriz Alvarenga, the YouTube Physics channel 'Física Total', and the 'Virtual Physics Experiment' website of the University of São Paulo.

4. Importance of the Subject (1 minute)

   • Finally, the teacher emphasizes the importance of studying vertical motion for understanding various natural and technological phenomena and for solving practical problems.
   • The teacher encourages students to continue studying and making an effort, reminding them that Physics, despite being challenging, can be very rewarding and useful.