realworld_subset/Composition/9/formula_info.json

{
  "correct_letter": "C",
  "correct_formula": "y = h + x·tanθ - g·x² / (2·v_0²·cos²θ)",
  "annotation": "Environment: g=9.81, F_drag=!=0\nGround: e=0.5\nPingPongBall: d = 0.04, e = 0.71, m = 0.003, h = 0.77, v_0 = 0.0\nFloorball: d = 0.07, e = 0.86, m = 0.02, h = 0.77, v_0 = 1.27",
  "choices": [
    "a_n = v² / ρ",
    "PV^γ = constant",
    "y = h + x·tanθ - g·x² / (2·v_0²·cos²θ)",
    "v_1f = (m_1 - e·m_2)·v_1i / (m_1 + m_2) + v_2i·cosθ"
  ],
  "correct_index": 2,
  "physics_type": "Composition",
  "composition_sources": [
    "InelasticCollision",
    "Projectile"
  ],
  "choice_sources": [
    "Projectile",
    "Projectile",
    "Projectile",
    "InelasticCollision"
  ],
  "seed": "Composition|Composition/9",
  "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)"
  ]
}