Dropped Garden Hose Whip

You build physics toys, and you have dropped a garden hose with the water on full.

Build me a single HTML page: a garden hose lying on a lawn, the spigot on, and the nozzle released.

The build

• A hose of fixed length, pinned at the spigot at one end, free at the nozzle end. It bends, carries mass, and does not stretch.
• Water pressure control shown on screen in psi, adjustable from 0 to full and back down.
• Water leaving the nozzle pushes back on it. At low pressure the hose settles. Past some pressure it starts to whip across the lawn. Lowering the pressure settles it again.
• Water particles exit along the current nozzle vector and land on the ground.
• Clicking and dragging pins that point of the hose to the mouse; releasing frees it.
• Loading the page as #psi=40 sets the pressure to 40 psi with the nozzle free on load. Any number works.
• The art is yours.

House rules

• One file. Everything inline — no CDN, no external stylesheet, font, script or image. data: URIs are fine.
• No libraries. No physics engine — write your own.
• No network at runtime.
• No localStorage, sessionStorage, cookies or indexedDB — sandboxed frame, they throw.
• Return the file as exactly one fenced html block.

Answer in exactly these sections

The model

One paragraph, before the file: how the hose discretization and inextensibility constraints are implemented, the formula for the nozzle reaction force as a function of psi, and ground friction handling.

The prediction

The pressure in psi at which the hose transitions from stationary or settling to continuous whipping, as one number, derived from your model parameters.

The page

The single fenced html block.

What it actually does

Where the motion looks like a real hose and where it does not. Name any artificial damping, injected noise or scripted oscillation. Everyone has watched a hose get away from somebody; say what yours gets wrong before I see it.