practice_algorithm_docs.md

Projectile Motion Simulation

This Python script simulates the motion of a projectile considering air resistance. It calculates and displays the horizontal distance traveled by the projectile before it hits the ground. The simulation accounts for gravity, air resistance, and user-defined initial conditions.

Code Structure

Constants

• g: Acceleration due to gravity (m/s^2).
• k: Air resistance constant (kg/s). Represents the drag on the projectile.
• m: Mass of the projectile (kg).

Initial Conditions

• x0, y0: Initial position (m) of the projectile (default: (0.0, 0.0)).
• v0: Initial velocity (m/s) of the projectile.
• theta: Launch angle in radians.

Calculations

• Calculates initial horizontal (v0x) and vertical (v0y) velocities.
• Defines time values for simulation from 0 to t_max seconds with a time step of dt.

Functions

• horizontal_motion(vx, t): Computes the horizontal velocity of the projectile at time t.
• vertical_motion(vy, t): Computes the vertical velocity of the projectile at time t.

Simulation

• Utilizes functional programming to update velocities over time.
• Finds the index when the projectile hits the ground (y = 0).
• Calculates the horizontal distance traveled when the projectile hits the ground.

Output

• Prints the horizontal distance traveled by the projectile.

Usage

To use this script, modify the initial conditions (e.g., v0, theta) as needed and run the script. The horizontal distance traveled will be displayed as output.

# Example: Modify initial conditions
v0 = 100.0  # Initial velocity (m/s)
theta = np.radians(45)  # Launch angle in radians

# Run the simulation
# ...

# Output will show the horizontal distance traveled

Output