I had several Parks water rockets when I was a kid (red single-stage, red two-stage, Gemini capsule & parachute with booster).

The Gemini capsule paracute was stored under the capsule during boost. When the rocket reached apogee and turned over, the capsule fell away and the parachute open (It really did work).

That boosted rocket coming in ballistic made quite a'thud' when it hit.

Bob