Optimal Launch Angle Finder

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Physics

Tranche

tranche-2

Evidence ID

t2-023

Ledger rows

1

No ledger note is attached.

Review findings

The supplied maximum-range angle formula is valid only for the stated vacuum maximum-range problem, not for the broader target-hitting claim. The instrument should either remove target-solving claims or add the projectile trajectory and target-angle equations, feasibility checks, and the complete range formula.

Formula and scope findings

• The level-ground optimum θ_max=45° is correct only for a vacuum projectile with equal launch and landing elevations, positive launch speed, and uniform positive gravitational acceleration.
• The height-offset formula θ=atan(v0/√(v0²+2gh0)) is correct for maximizing horizontal range when h0 is the launch height above the landing level, with v0>0, g>0, and h0≥0. These domain constraints are not stated.
• The specification claims the instrument can find an angle that hits a target, but no target-trajectory equation or target-angle solution is provided. Hitting a target generally yields zero, one, or two feasible angles depending on distance, height, speed, and constraints.
• The specification claims to output resulting range, but no range formula is provided. The required vacuum-model range formula is R=(v0 cosθ/g)(v0 sinθ+√(v0²sin²θ+2gh0)); at the maximizing angle for h0≥0 this simplifies to R_max=(v0/g)√(v0²+2gh0).
• The formula does not define behavior for h0<0, v0=0, g≤0, or v0²+2gh0≤0.

Unit assumptions

• Use a consistent unit system: v0 in m/s, g in m/s², h0 and range in m, and angles in degrees for display.
• The example with v0=72 km/h requires conversion to 20 m/s before applying the formula.
• g is uniform gravitational acceleration and is normally 9.81 m/s² near Earth.
• atan returns an angle in radians internally; convert to degrees for the displayed angle.
• h0 means launch height above the landing level, not an arbitrary signed height offset.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The height h0=-v0^2/(2g) makes sqrt(v0^2+2gh0)=0, so the angle formula divides by zero and the expected result is undefined. The instrument should reject this input.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "v0": 20,
    "g": 9.81,
    "h0": 0,
    "units": "SI"
  },
  "expected_outputs": {
    "optimal_angle_deg": 45,
    "resulting_range_m": 40.7747
  },
  "working": "θ=atan(20/√(20²+2×9.81×0))=atan(20/20)=atan(1)=45°. R_max=(20/9.81)×√(20²+0)=(20/9.81)×20=400/9.81=40.7747 m."
}

Related workflows

Sources and evidence

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

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