Lesson Plan | Traditional Methodology | Kinematics: Vertical Motion

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage is to present the specific objectives of the lesson to the students, ensuring that they understand what will be learned and developed throughout the session. This way, students will have a clear vision of what is expected of them by the end of the class, facilitating content absorption and the practical application of kinematic concepts in vertical motion.

Main Objectives

1. Describe the concept of vertical motion, including free fall and vertical launch.

2. Calculate the distance traveled, final speed, and time of displacement of an object in vertical motion.

3. Apply specific mathematical formulas to solve problems related to vertical motion.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage is to capture the students' attention and introduce the theme of vertical motion in an engaging and relevant way. By contextualizing the content and presenting curiosities, the aim is to spark students' interest and prepare them for the understanding of the concepts that will be covered throughout the lesson.

Context

To begin the class on vertical motion, explain to students that the study of kinematics is essential for understanding how objects move in the world around us. Vertical motion is a fundamental part of kinematics, as it involves the analysis of objects that move up or down under the influence of gravity. This type of motion can be observed in everyday situations, such as a ball being thrown upwards or an object falling from a certain height. Understanding these concepts will help students solve practical problems and better understand natural phenomena.

Curiosities

Did you know that Galileo Galilei conducted experiments with free-falling objects, challenging the prevailing ideas of his time? He supposedly dropped two spheres of different masses and observed that they hit the ground at the same time, helping to establish the theory that all objects, regardless of their mass, fall with the same acceleration in the absence of air resistance.

Development

Duration: (40 - 50 minutes)

The purpose of this stage is to provide a detailed and practical understanding of the concepts of vertical motion. By addressing specific topics with clear examples and practical exercises, students will have the opportunity to apply mathematical formulas and solve real problems. This will consolidate theoretical knowledge and develop essential skills for calculating distances, times, and speeds in vertical movements.

Covered Topics

1. Concept of Vertical Motion: Explain what vertical motion is, highlighting the concepts of free fall and vertical launch. Emphasize that vertical motion is influenced by gravity, which acts as a constant force. 2. Equations of Vertical Motion: Present and explain the fundamental equations used to calculate distance (S), final speed (Vf), and time of displacement (t) of an object in vertical motion. The main equations are: S = S0 + V0t + (1/2)gt², Vf = V0 - gt, and Vf² = V0² + 2g(S - S0), where S0 is the initial position, V0 is the initial speed, g is the acceleration due to gravity, and t is the time. 3. Practical Examples: Provide detailed practical examples to illustrate how to apply the equations of vertical motion. For instance, calculate the height of a tower from which an object is released and the time it takes to reach the ground. 4. Air Resistance: Briefly address the effect of air resistance on vertical motion, explaining how air resistance can alter results in real situations compared to theoretical calculations. Highlight that, for simplification, initial calculations usually disregard air resistance.

Classroom Questions

1. An object is launched vertically upwards with an initial speed of 20 m/s. Calculate the maximum height reached by the object and the time it takes to reach that height. 2. A ball is dropped from the top of a 50-meter tall building. How long does it take to reach the ground? What is the speed of the ball when it hits the ground? 3. If an object is launched downwards with an initial speed of 5 m/s from a height of 30 meters, what will be the speed of the object when it hits the ground?

Questions Discussion

Duration: (20 - 25 minutes)

The purpose of this stage is to review and consolidate the knowledge acquired by students during the class, ensuring that they understand the concepts and formulas presented. The detailed discussion of the questions and student engagement through questions and reflections help to reinforce content, identify possible doubts, and promote a deeper and more meaningful learning experience.

Discussion

• Question 1: An object is launched vertically upwards with an initial speed of 20 m/s. Calculate the maximum height reached by the object and the time it takes to reach that height.

• To solve this question, first use the formula to calculate the maximum height (S):

• S = (V0²) / (2g)

• Where V0 is the initial speed (20 m/s) and g is the acceleration due to gravity (approximately 9.8 m/s²).

• Substituting the values: S = (20²) / (2 * 9.8) = 400 / 19.6 ≈ 20.4 meters.

• To calculate the time (t) it takes to reach that height, use the formula:

• Vf = V0 - gt

• Since the final speed (Vf) at the highest point is 0: 0 = 20 - 9.8t => t = 20 / 9.8 ≈ 2.04 seconds.

• Question 2: A ball is dropped from the top of a 50-meter tall building. How long does it take to reach the ground? What is the speed of the ball when it hits the ground?

• To calculate the time (t) it takes for the ball to reach the ground, use the formula:

• S = (1/2)gt²

• Where S is the height (50 meters), and g is the acceleration due to gravity (9.8 m/s²).

• 50 = (1/2) * 9.8 * t² => t² = 50 / 4.9 => t² ≈ 10.2 => t ≈ 3.19 seconds.

• To calculate the speed (Vf) when hitting the ground, use the formula:

• Vf = gt

• Substituting the values: Vf = 9.8 * 3.19 ≈ 31.26 m/s.

• Question 3: If an object is launched downwards with an initial speed of 5 m/s from a height of 30 meters, what will be the speed of the object when it hits the ground?

• To calculate the speed (Vf) when hitting the ground, use the formula:

• Vf² = V0² + 2g(S - S0)

• Where V0 is the initial speed (5 m/s), g is the acceleration due to gravity (9.8 m/s²), and S - S0 is the height (30 meters).

• Substituting the values: Vf² = 5² + 2 * 9.8 * 30 => Vf² = 25 + 588 => Vf² = 613 => Vf ≈ 24.76 m/s.

Student Engagement

1. Ask the students: 'How would air resistance alter the results obtained?' 2. Question: 'If gravity's acceleration were different, how would that affect the motion of objects?' 3. Ask students to discuss in groups: 'How can we apply the concepts of vertical motion in sports or other daily activities?' 4. Encourage students to reflect: 'What are the limitations of the mathematical models we use to describe vertical motion?'

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to review and consolidate the main points of the lesson, ensuring that students have a clear and organized view of the content learned. Additionally, it reinforces the connection between theory and practice, highlighting the significance of the topic in daily life and in various applications.

Summary

• Concept of vertical motion, including free fall and vertical launch.
• Fundamental equations for calculating distance, final speed, and time of displacement in vertical motion.
• Detailed practical examples to illustrate the application of the equations.
• Discussion on air resistance and its implications in vertical motion.

The class connected theory with practice by using real examples and step-by-step solved problems, allowing students to see how mathematical formulas apply to everyday situations, such as throwing a ball or the fall of an object from a specific height.

Understanding vertical motion is fundamental to various fields, from structural engineering to sports and recreational activities. Knowing how to correctly calculate the time of fall and the speed of an object can be crucial in practical situations, such as predicting the impact of falling objects or optimizing launches in sports.