Source: https://guthlabs.ai/docs/instruments/projectile-motion-solver/implementation/

instrument implementation / implementation-contract

# Projectile Motion Solver implementation

A source-bound implementation contract for Projectile Motion Solver; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t6-084

**Effect**: Computation or source lookup only

## Input and validation requirements

The optional-drag branch is not reproducible from the specification because its numerical integration settings and drag-vector interpretation are unspecified. The solver also needs explicit validation for zero mass and explicit angle units; otherwise it can produce undefined or physically nonsensical results.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "mode": "no_drag",
    "v0_m_per_s": 20,
    "angle_deg": 45,
    "launch_height_m": 0,
    "g_m_per_s2": 9.81,
    "sample_x_m": [
      0,
      10,
      20,
      40.77472
    ]
  },
  "expected_outputs": {
    "range_m": 40.77472,
    "max_height_above_launch_m": 10.19368,
    "absolute_max_height_m": 10.19368,
    "flight_time_s": 2.883208,
    "trajectory_y_m": [
      0,
      7.5475,
      10.19,
      0
    ],
    "apex_x_m": 20,
    "roots_m": [
      0,
      40.77472
    ]
  },
  "working": "Convert angle: theta=45*pi/180=pi/4. sin(theta)=sqrt(2)/2 and sin(2theta)=1. Range=(20^2)(1)/9.81=400/9.81=40.77472 m. Maximum height=20^2(0.5)/(2*9.81)=200/19.62=10.19368 m. Flight time=2*20*(sqrt(2)/2)/9.81=28.284271/9.81=2.883208 s. With y(x)=x*tan(theta)-g*x^2/(2*v0^2*cos^2(theta))=x-9.81*x^2/400: y(0)=0; y(10)=10-981/400=7.5475 m; y(20)=20-3924/400=10.19 m; y(40.77472) is approximately 0. The apex occurs at half the range, x=20 m."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/projectile-motion-solver/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/projectile-motion-solver/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/projectile-motion-solver/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche6/tranche6-results.json`