Fireworks projectile motion - 2D side view

A rocket decelerates under gravity, bursts near its apex, and the star cloud follows parabolas while its centre falls.

Switch to 3D

Presets

Playback

Rocket

Burst

Click or tap the sky to launch from that spot.

Model checks

The science

Rocket climb

The rocket leaves the ground with vertical speed v0 and decelerates at gr = 20 m/s² (the 3D page value). Its height and speed are y = v0t − ½ gr t², v = v0 − grt. The shell explodes when v ≤ 2 m/s or when the target height is reached, so the burst height without a cap is yb = (v0² − 4)/(2 gr).

Burst shell

Stars leave in all directions with speeds 18 to 40 m/s. Each star follows a parabola; with vertical gravity gb = 12 m/s² the whole cloud keeps its shape but its centre falls by ½ gb t². The 3D page also damps the horizontal velocity by 2 % per frame, i.e. vx(t) = vx0 e−kt with k = −60 ln 0.98 = 1.21 s−1, so horizontal reach saturates at vx0/k.

Honest simplifications: a 2D slice of a 3D sphere of stars (stars moving along the viewing axis are projected), no air drag on the vertical motion, no wind, stars simply fade (no burning-rate or colour chemistry). This is a physics demonstration of ballistics, not a pyrotechnic design guide.

What to try
  • Click the sky to launch from a chosen spot and watch the burst height match the prediction.
  • Moon fireworks: weak gravity gives huge slow bursts.
  • Switch horizontal damping off: the burst becomes a perfect falling sphere.
Rocket height against time
Burst radius, centre drop and damped reach
Star speed distribution