Each shot integrates Newton's second law directly: gravity pulls straight down at g, and a linear air-drag force F = −k·v opposes the velocity vector, so the trajectory is computed step by step rather than drawn as a fixed parabola:
vx' = −k·vx
vy' = −g − k·vy
x' = vx, y' = vy
With k = 0 this reduces to the textbook drag-free parabola, whose range has the closed form R = v₀²·sin(2θ)/g — shown live as "Ideal range" so you can compare it against the real, drag-damped flight path traced on the range. Increasing drag visibly shortens the range and steepens the descent angle relative to the launch angle, which is exactly what real ballistic drag does and a pure parabola formula cannot show.
- Launch angle / speed — set the muzzle direction and initial velocity magnitude.
- Gravity — switch between Earth, Moon and Mars, or drag freely to any value.
- Air drag (k) — 0 is vacuum; higher values model a light, high-drag projectile (e.g. a foam ball) rather than a bullet.