Projectile Motion Simulation

This tool simulates the ideal parabolic trajectory of a projectile launched at an angle in a uniform gravitational field with no air resistance.

Users enter initial velocity, launch angle, gravitational acceleration, and initial height. The tool calculates time of flight, range, maximum height, and component velocities using classical mechanics equations.

The key equations are:

Horizontal motion (constant velocity):   \[ x = v_0 \cos\theta \cdot t \]

Vertical motion (constant acceleration):   \[ y = h_0 + v_0 \sin\theta \cdot t - \frac{1}{2} g t^2 \]

Time of flight (solving for y = 0):   \[ t = \frac{v_0 \sin\theta + \sqrt{(v_0 \sin\theta)^2 + 2 g h_0}}{g} \]

Range:   \[ R = v_0 \cos\theta \cdot t \]

Maximum height:   \[ H = h_0 + \frac{(v_0 \sin\theta)^2}{2 g} \]

The tool displays the complete trajectory with launch and landing points, supports interactive exploration, 3D visualization, auto-playing animation, and manual play/pause control.

Ideal for teaching kinematics, optimizing launch parameters, understanding planetary differences in gravity, and educational physics demonstrations.