physics simulation
Projectile Motion
Interactive simulator exploring launch angles, gravity, and air resistance on projectile trajectories.
How to use: Adjust initial velocity, launch angle, gravity, and air drag. Watch the trajectory update in real-time. Press LAUNCH to animate the projectile motion.
Initial Velocity (m/s)
45
Launch Angle (°)
45
◆ Optimal range: 45°
Gravity Preset
Air Drag (k/m)
0.00
Launch Height (m)
0
Simulation Speed
1.0×
Range (no drag):
88.7 m
Max Height:
51.6 m
Time of Flight:
6.48 s
Launch Velocity:
45.0 m/s
| Planet | Range (m) | Height (m) |
|---|---|---|
| Earth | 88.7 | 51.6 |
| Moon | 533.0 | 309.6 |
| Mars | 239.8 | 139.2 |
| Jupiter | 33.1 | 19.2 |
Equations & Formulas
Without Air Drag:
x(t) = v₀cos(θ) · t
y(t) = v₀sin(θ) · t − ½g · t²
Range: R = v₀²sin(2θ)/g
Max Height: H = v₀²sin²(θ)/(2g)
Time of Flight: T = 2v₀sin(θ)/g
With Air Drag:
F_drag = ½ρCdA · v²
aₓ = −(k/m) · vₓ · |v|
aᵧ = −g − (k/m) · vᵧ · |v|
x(t) = v₀cos(θ) · t
y(t) = v₀sin(θ) · t − ½g · t²
Range: R = v₀²sin(2θ)/g
Max Height: H = v₀²sin²(θ)/(2g)
Time of Flight: T = 2v₀sin(θ)/g
With Air Drag:
F_drag = ½ρCdA · v²
aₓ = −(k/m) · vₓ · |v|
aᵧ = −g − (k/m) · vᵧ · |v|