Physical Principles & Mathematical Derivation
When launching from a cliff or tower of height h₀ > 0, extra fall distance favors higher horizontal velocity vx₀, shifting the maximum-range angle θ_opt = arcsin(v₀ / √(2v₀² + 2gh₀)) below 45°.
Questions & Concepts
What physical equation governs Elevated Tower & Cliff Projectile Motion Simulator?
t_flight = [ vy0 + √(vy0² + 2·g·h0) ] / g — When launching from a cliff or tower of height h₀ > 0, extra fall distance favors higher horizontal velocity vx₀, shifting the maximum-range angle θ_opt = arcsin(v₀ / √(2v₀² + 2gh₀)) below 45°.
How are the equations of motion integrated in this simulation?
Nonlinear differential equations are integrated at 240–300 Hz substeps using classical 4th-order Runge-Kutta (RK4) to maintain strict Hamiltonian energy accuracy.