The Ballistics & Drag Lab — Projectile Motion vs. Vacuum

Ideal Vacuum

Quadratic Drag

Earth: g=9.81 m/s², ρ=1.225 kg/m³

v⃗ Velocity F⃗_d Drag F⃗_g Gravity

Force Vectors

100% | Scroll/Drag to Pan

t = 0.00 s Ready

Apex Height (y_max) 0.0%

DRAG 0.00 m

VACUUM 0.00 m

Range (x_max) 0.0%

DRAG 0.00 m

VACUUM 0.00 m

Time of Flight 0.0%

DRAG 0.00 s

VACUUM 0.00 s

Live / Impact Speed v_t: 46.6 m/s

DRAG 50.0 m/s

VACUUM 50.0 m/s

1. Planetary Environment

g & ρ presets

2. Launch Kinematics

Initial Velocity (v₀)

50.0 m/s

The muzzle speed of the projectile at launch. Higher speeds quadratically amplify air resistance force (F_d ∝ v²).

10 m/s 55 m/s 100 m/s

Launch Angle (θ)

45.0°

Angle relative to the horizontal ground. In a vacuum, 45° yields maximum range; with drag, the optimal angle shifts lower.

0° (Flat) 45° (Max Vacuum) 90° (Vertical)

3. Projectile & Drag

A = 0.0314 m²

Projectile Mass (m)

2.0 kg

Inertia of the projectile (a_drag = F_d/m). Heavier objects resist air deceleration much better than light objects.

0.1 kg 25 kg 50 kg

Radius (r) [A = πr²]

0.10 m

Determines cross-sectional frontal area (A). Larger radius catches more air molecules, increasing drag forces.

0.02 m 0.25 m 0.50 m

Drag Coefficient (C_d)

0.47

Aerodynamic streamlined shape factor. Low values (0.3) mean slippery shapes like bullets; high values (1.05) mean blunt flat surfaces like cubes.

Key Physics Insights

Unlike vacuum motion where mass cancels out (a = -g), aerodynamic deceleration scales inversely with mass (a_d = F_d/m). Lighter or wider projectiles lose horizontal momentum rapidly, creating an asymmetric path with a steeper descent!

F_d = ½ρC_dAv² v_t = √(2mg / ρC_dA)