Projectile Launcher Simulation Documentation

This document provides a comprehensive guide for the Projectile Launcher Simulation. The simulation visualizes the trajectory of a projectile launched at a specified angle and speed, allowing users to modify key parameters such as gravity, initial velocity, and launch angle. In addition, a real‑time graph plots data like position, velocity components, and overall speed.

Overview

The Projectile Launcher Simulation is designed to help you explore the dynamics of projectile motion. The interface consists of:

  • A simulation area that displays a red projectile launched from a fixed starting point above a ground line. An overlay shows the current frames per second (FPS) for performance monitoring.
  • A graph panel where Chart.js dynamically plots selected parameters over time. Use dropdown menus to switch between variables such as time, x and y positions, horizontal and vertical velocity, and speed.
  • A controls panel with sliders to adjust the gravity (in px/s²), the initial velocity (in px/s), and the launch angle (in degrees). Buttons are provided to start, pause, and reset the simulation.

How to Use the Simulation

When the simulation is launched, you can interact with the following sections:

  • Simulation Area:
    The projectile is launched from a starting point (50 px from the left and slightly above the ground) and follows a curved path determined by its initial velocity and gravity. The ground is represented by a horizontal line, and when the projectile hits the ground, its motion stops.

  • Graph Panel:
    Real-time data is plotted on a scatter chart. The x‑ and y‑axes can be set independently to show variables such as time, x position, y position, horizontal velocity, vertical velocity, and speed. This graphical representation helps illustrate changes in the projectile’s motion over time.

  • Controls Panel:
    Users can modify three primary parameters using slider inputs:

  • Gravity: Adjusts the gravitational acceleration (default is 981 px/s²).
  • Initial Velocity: Sets the launch speed (default is 500 px/s).
  • Launch Angle: Determines the angle at which the projectile is launched (default is 45°).
    • Start: Begins the simulation.
    • Pause: Temporarily halts the simulation.
    • Reset: Returns the simulation variables to their original settings and clears the graph.

Physics Behind the Simulation

The simulation models the basic physics of projectile motion using the following principles:

  • Initial Velocity Decomposition:
    When the projectile is launched, its velocity is split into horizontal and vertical components based on the launch angle:
\[ v_x = v_0 \cos(\theta) \quad \text{and} \quad v_y = -v_0 \sin(\theta) \]

(Note: In canvas coordinates, upward motion is negative.)

  • Motion Update:
    The projectile’s position is updated over time using the equations:
\[ x(t) = x_0 + v_x \cdot t \]
\[ y(t) = y_0 + \int_{0}^{t} \bigl( v_y + g \, t' \bigr) dt' \]

where \( g \) is the gravitational acceleration. The simulation applies \( g \) on each update step.

  • Collision Detection:
    When the projectile’s y-coordinate exceeds the ground level, the simulation stops its vertical motion. The ground is drawn as a horizontal line near the bottom of the simulation area.

Educational Insights

The Projectile Launcher Simulation offers several learning opportunities:

  • Parameter Exploration:
    By adjusting gravity, initial velocity, and launch angle, you can observe how each factor influences the trajectory. Experiment with extreme values to see the effect on both flight duration and range.

  • Visualization of Motion:
    Watch the curved path of the projectile and correlate it with the underlying physics. The real‑time graph reinforces how speed, and both horizontal and vertical velocities, evolve over time.

  • Real-Time Data Analysis:
    The simulation collects data on time, position, and velocity components. Observing these datasets helps to solidify concepts related to kinematics and projectile motion.

Conclusion

The Projectile Launcher Simulation provides an engaging and interactive way to study the principles of projectile motion. By experimenting with different parameters and observing the real‑time dynamics and graphs, users can deepen their understanding of motion under gravity. Enjoy exploring the fascinating aspects of projectile physics and refining your analytical skills through simulation!