Overview

This app analyzes ideal projectile motion (no air resistance). Provide the initial speed, launch angle (in degrees), and gravitational acceleration. The app computes the maximum height, total flight time, and horizontal range, then plots the trajectory and animates the projectile moving from launch to landing.

Formulas

• Maximum height: $H = \dfrac{v_0^2\,\sin^2(\theta)}{2\,g}$
• Time of flight: $T = \dfrac{2\,v_0\,\sin(\theta)}{g}$
• Horizontal range: $R = \dfrac{v_0^2\,\sin(2\theta)}{g}$

Trajectory equation $y(x)$ (for $\cos(\theta) \ne 0$): $y = xtan(\theta) - \dfrac{g,x^2}{2\,v_0^2\,\cos^2(\theta)}$.

Angles are supplied in degrees $^\circ$ and converted to radians internally. For vertical launches ($\theta = 90^\circ$), the parametric form $x(t) = v_0\cos(\theta)\,t$, $y(t) = v_0\sin(\theta)\,t - \tfrac{1}{2} g t^2$ is used to generate the plot and animation.

How to Use

• Set the Initial velocity $v_0$ in m/s.
• Set the Launch angle $\theta$ in degrees $^\circ$.
• Optionally adjust Gravity $g$ (default $9.81\,\text{ m/s}^2$).
• Read the computed Maximum height $H$, Time of flight $T$, and Range $R$.
• See the Diagram for the trajectory and the Animation to watch the projectile move until it lands.

Notes

• The model assumes a flat launch and landing elevation and no aerodynamic drag.
• For zero or near-zero values (e.g., $v_0 = 0$), the plot and animation will default to minimal ranges to remain visible.