realworld_subset/Composition/0/formula_info.json

{
  "correct_letter": "D",
  "correct_formula": "y = h + x·tanθ - g·x² / (2·v_0²·cos²θ)",
  "annotation": "Environment: g=9.81, F_drag=!=0\nGround: e=0.5\nTennisBall: d = 0.07, e = 0.75, m = 0.06, h = 0.77, v_0 = 0.0\nSteelBall: d = 0.04, e = 0.6, m = 0.26, h = 0.77, v_0 = 1.12",
  "choices": [
    "v_cm = (m_1·v_1i² + m_2·v_2i²) / (m_1·v_1i + m_2·v_2i)",
    "T = 2π·√(m/k)",
    "h_next = e²·h_current",
    "y = h + x·tanθ - g·x² / (2·v_0²·cos²θ)"
  ],
  "correct_index": 3,
  "physics_type": "Composition",
  "composition_sources": [
    "InelasticCollision",
    "Projectile"
  ],
  "choice_sources": [
    "InelasticCollision",
    "InelasticCollision",
    "Projectile",
    "Projectile"
  ],
  "seed": "Composition|Composition/0",
  "is_realworld": true,
  "dropped_wrong_formulas": [
    "InelasticCollision: W_f = ∫ μ_k·m·g·ds = ΔE_k",
    "Projectile: F_drag = (1/2)·C_d·ρ·A·v² (A = π·(d/2)²)"
  ]
}