Relative Velocity Composition (classical) mechanism

Model scope

The classical vector-addition formula itself is correct under the stated velocity-frame convention, and the honest non-relativistic label is appropriate. The specification needs an explicit vector-angle convention and must either rename the heading output to 'resultant heading' or add the target vector and frame information needed to compute a heading required to reach that target.

• The formula v_AC = v_AB + v_BC is standard only when v_XY explicitly means the velocity of X relative to Y; that notation convention is not stated.
• The claimed output 'heading needed to reach target' is not computable from only two velocity vectors unless a target velocity/vector, target frame, and desired heading definition are also provided. The resultant heading is not necessarily the heading required to reach a target.

Units and conventions

• Both input velocities must use the same units before addition; components cannot be added directly across mixed units.
• Directions are assumed to be bearings measured counterclockwise from the positive east/x axis, with vector components computed as x = v cos(theta) and y = v sin(theta). A compass UI must explicitly document its bearing convention.
• The reported resultant magnitude has the same velocity unit as the inputs.
• The formula is Galilean/non-relativistic and is appropriate when relativistic effects are negligible.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "v_AB": {
      "magnitude": 8,
      "unit": "m/s",
      "direction_deg_from_east_ccw": 0
    },
    "v_BC": {
      "magnitude": 3,
      "unit": "m/s",
      "direction_deg_from_east_ccw": 90
    }
  },
  "expected_outputs": {
    "resultant_x": 8,
    "resultant_y": 3,
    "resultant_magnitude_m_per_s": 8.544004,
    "resultant_heading_deg_from_east_ccw": 20.556045
  },
  "working": "v_AB = (8 cos 0°, 8 sin 0°) = (8, 0) m/s. v_BC = (3 cos 90°, 3 sin 90°) = (0, 3) m/s. Sum = (8 + 0, 0 + 3) = (8, 3) m/s. Magnitude = sqrt(8^2 + 3^2) = sqrt(64 + 9) = sqrt(73) = 8.544004 m/s. Heading = atan2(3, 8) = 20.556045°."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The extreme-magnitude vector pair overflows JavaScript Number arithmetic to Infinity, so the instrument must reject or explicitly report a non-finite result. The specification also leaves angular sign and heading-wrap conventions unspecified, producing reflected or differently represented headings.

Other records

Sources and evidence

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

• VERIFIED_LEDGER.json
• evidence-tranche2/tranche2-results.json
• BOUNDARY_HAZARD_CATALOG.json