Contoh soal gerak vertikal ke atas dan pembahasan

Introduction

This tutorial provides a step-by-step guide to solving vertical motion problems, specifically focusing on projectiles thrown upwards. Using examples from the video "Contoh soal gerak vertikal ke atas dan pembahasan," we will explore the physics concepts involved, including calculating maximum height and initial velocity.

Step 1: Understanding the Problem

Before solving any problem, it’s essential to grasp the key concepts:

• Vertical Motion: This involves objects moving up and down under the influence of gravity.
• Acceleration due to Gravity (g): This is typically -9.81 m/s² (downward), but for simplicity, we will use -10 m/s² as in the video.
• Initial Velocity (v₀): The speed at which the object is thrown upwards.

Step 2: Example Problem 1 - Calculating Maximum Height

Problem Statement

A ball is thrown vertically upwards with an initial speed of 20 m/s. Calculate the maximum height reached by the ball.

Steps to Solve

1. Use the formula for maximum height (h): [ h = \frac{v₀^2}{2g} ]

2. Plug in the values:

   • Initial speed (v₀) = 20 m/s
   • Acceleration due to gravity (g) = 10 m/s²

   The calculation becomes: [ h = \frac{(20)^2}{2 \times 10} = \frac{400}{20} = 20 \text{ m} ]

3. Conclusion for this example: The maximum height reached by the ball is 20 meters.

Step 3: Example Problem 2 - Finding Initial Velocity

Problem Statement

A stone is thrown upwards and returns to the starting point after 4 seconds. Calculate the initial velocity of the stone.

Steps to Solve

1. Understand the motion: The total time of flight (T) is the time taken to go up and come back down. Hence, the time to reach the maximum height is T/2. Here, T = 4 seconds, so:

   • Time to reach maximum height = 4/2 = 2 seconds.

2. Use the formula for time of flight: The formula relating initial velocity (v₀) and time to reach maximum height (t) is: [ v₀ = g \times t ]

3. Plug in the values:

   • g = 10 m/s²
   • t = 2 s

   The calculation becomes: [ v₀ = 10 \times 2 = 20 \text{ m/s} ]

4. Conclusion for this example: The initial velocity of the stone is 20 m/s.

Conclusion

In this tutorial, we covered how to solve vertical motion problems involving projectiles. Key takeaways include:

• Understanding the principles of vertical motion, including how to calculate maximum height and initial velocity.
• Applying the formulas appropriately for practical problems.

For further practice, try solving additional problems using the same methods. Experiment with different values for initial velocity and time to deepen your understanding of vertical motion physics.