Projectile motion with air drag

What you are seeing: three projectiles fired simultaneously at the same speed $v_0$ and angle $\theta$, subject to different drag laws. The yellow projectile is in vacuum (no drag); the cyan one experiences Stokes drag $F = -b\mathbf{v}$; the orange one experiences quadratic drag $F = -c|\mathbf{v}|\mathbf{v}$. All three leave the launcher at the same time but land at different ranges.

Without drag the trajectory is a parabola with range $R = v_0^2 \sin(2\theta) / g$ (max at $\theta = 45^\circ$). Stokes drag is linear and falls off more gently with speed; quadratic drag grows faster at high speed, so it bites harder near launch. Slide the speed and angle to see the asymmetry: at high speeds quadratic drag dominates; at low speeds Stokes drag wins.