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.