2D Kinematics Equations: Horizontal motion has zero acceleration: $x(t) = v_0 \cos\theta \cdot t$. Vertical motion undergoes gravitational acceleration: $y(t) = h_0 + v_0 \sin\theta \cdot t - \frac{1}{2}gt^2$.
Maximum Height (Apogee): Vertical velocity reaches zero ($v_y = 0$) at peak height $H = h_0 + \frac{(v_0\sin\theta)^2}{2g}$.
Horizontal Range & Flight Time: From ground level ($h_0 = 0$), total flight time is $t = \frac{2v_0\sin\theta}{g}$ and total range is $R = \frac{v_0^2\sin 2\theta}{g}$, maximized at launch angle $\theta = 45^\circ$.
Operating Instructions: Set initial launch velocity $v_0$, angle $\theta$, height $h_0$, and gravity $g$. Launch to trace ballistic trajectory parabolas and kinematic metrics.