Projectile Motion Simulator

This Lua script models the motion of a projectile launched at a specific angle and initial velocity. It calculates key details of the parabolic trajectory, including:

• Maximum height
• Horizontal range
• Time of flight

Features

• Simulates the projectile's motion with gravity and an optional initial height.
• Computes key points of the parabola, such as the vertex and roots.
• Measures execution time for performance analysis.

How It Works

The script uses a quadratic equation to represent the trajectory: [ y = ax^2 + bx + c ] Where:

• ( a ): determined by gravity and initial velocity.
• ( b ): determined by the launch angle.
• ( c ): initial height.

Iterative calculations are performed to determine the point where the projectile hits the ground.

How to Run

1. Save the script as projectile_motion.lua.
2. Ensure Lua is installed on your system.
3. Run the script in your terminal:

   lua projectile_motion.lua