Ecrit par ✅ Quiz : Mouvement Des Projectiles
Ce quiz contient 20 questions.
Note : Placeholder pour valider la structure. Le JSON converti est conservé ci-dessous pour l’import final des vraies questions Tutor LMS.
JSON Tutor LMS-ready
{
"quiz_title": "Mouvement Des Projectiles",
"quiz_slug": "06_mouvement_des_projectiles_quiz",
"quiz_description": "Quiz Edu509 : Mouvement Des Projectiles",
"quiz_settings": {
"time_limit": {
"time_value": 0,
"time_type": "minutes"
},
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"attempts_allowed": 0,
"passing_grade": 70,
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},
"questions": [
{
"question_order": 1,
"question_title": "Un projectile est lancé avec une vitesse initiale de \\\\(v_0 = 20\\\\,\\\\mathrm{m/s}\\\\) sous un angle de \\\\(45^\\\\circ\\\\) par rapport à l’horizontale. Quelle est la portée maximale du projectile ? (\\\\(g = 9{,}8\\\\,\\\\mathrm{m/s^2}\\\\))",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La portée maximale est donnée par \\\\(R = \\\\frac{v_0^2 \\\\sin(2\\\\theta)}{g}\\\\). Ici, \\\\(\\\\sin(90^\\\\circ) = 1\\\\), donc \\\\(R = \\\\frac{20^2 \\\\times 1}{9{,}8} = \\\\frac{400}{9{,}8} \\\\approx 40,8\\\\,\\\\mathrm{m}\\\\).",
"answers": [
{
"answer_title": "40,8 m",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "20,4 m",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "28,6 m",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "10,2 m",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 2,
"question_title": "Un projectile est lancé à \\\\(v_0 = 15\\\\,\\\\mathrm{m/s}\\\\) sous un angle de \\\\(30^\\\\circ\\\\). Quelle est la hauteur maximale atteinte ? (\\\\(g = 9{,}8\\\\,\\\\mathrm{m/s^2}\\\\))",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La hauteur maximale est \\\\(H_{max} = \\\\frac{v_0^2 \\\\sin^2(\\\\theta)}{2g}\\\\). \\\\(\\\\sin(30^\\\\circ) = 0,5\\\\), donc \\\\(H_{max} = \\\\frac{15^2 \\\\times 0,25}{19,6} = \\\\frac{56,25}{19,6} \\\\approx 2,87\\\\,\\\\mathrm{m}\\\\).",
"answers": [
{
"answer_title": "4,3 m",
"is_correct": false,
"answer_order": 1
},
{
"answer_title": "8,6 m",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "2,9 m",
"is_correct": true,
"answer_order": 3
},
{
"answer_title": "5,7 m",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 3,
"question_title": "Pour un projectile lancé du sol avec \\\\(v_0 = 10\\\\,\\\\mathrm{m/s}\\\\) sous \\\\(60^\\\\circ\\\\), combien de temps reste-t-il en l’air ? (\\\\(g = 9{,}8\\\\,\\\\mathrm{m/s^2}\\\\))",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le temps de vol est \\\\(T = \\\\frac{2 v_0 \\\\sin(\\\\theta)}{g}\\\\). \\\\(\\\\sin(60^\\\\circ) = 0,866\\\\), donc \\\\(T = \\\\frac{2 \\\\times 10 \\\\times 0,866}{9,8} = \\\\frac{17,32}{9,8} \\\\approx 1,77\\\\,\\\\mathrm{s}\\\\).",
"answers": [
{
"answer_title": "1,77 s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "1,02 s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "2,12 s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "1,50 s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 4,
"question_title": "Un projectile est lancé horizontalement à \\\\(v_0 = 12\\\\,\\\\mathrm{m/s}\\\\) depuis une hauteur de \\\\(h_0 = 10\\\\,\\\\mathrm{m}\\\\). Combien de temps met-il à toucher le sol ? (\\\\(g = 9{,}8\\\\,\\\\mathrm{m/s^2}\\\\))",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "Le temps de chute verticale est \\\\(t = \\\\sqrt{\\\\frac{2 h_0}{g}} = \\\\sqrt{\\\\frac{20}{9,8}} \\\\approx 1,43\\\\,\\\\mathrm{s}\\\\).",
"answers": [
{
"answer_title": "1,43 s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "2,02 s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "0,98 s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "1,02 s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 5,
"question_title": "Un projectile est lancé à \\\\(v_0 = 25\\\\,\\\\mathrm{m/s}\\\\) sous un angle de \\\\(0^\\\\circ\\\\). Quelle est la portée maximale ? (\\\\(g = 9{,}8\\\\,\\\\mathrm{m/s^2}\\\\))",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "À \\\\(0^\\\\circ\\\\), \\\\(\\\\sin(0) = 0\\\\), donc la portée est nulle : \\\\(R = 0\\\\,\\\\mathrm{m}\\\\).",
"answers": [
{
"answer_title": "0 m",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "31,9 m",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "63,8 m",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "12,5 m",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 6,
"question_title": "Un projectile est lancé à \\\\(v_0 = 18\\\\,\\\\mathrm{m/s}\\\\) sous \\\\(40^\\\\circ\\\\). Quelle est la portée maximale ? (\\\\(g = 9{,}8\\\\,\\\\mathrm{m/s^2}\\\\))",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La portée maximale est \\\\(R = \\\\frac{v_0^2 \\\\sin(2\\\\theta)}{g}\\\\). \\\\(\\\\sin(80^\\\\circ) = 0,984\\\\), donc \\\\(R = \\\\frac{324 \\\\times 0,984}{9,8} = \\\\frac{318,816}{9,8} \\\\approx 32,5\\\\,\\\\mathrm{m}\\\\).",
"answers": [
{
"answer_title": "32,5 m",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "25,8 m",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "18,0 m",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "36,2 m",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 7,
"question_title": "Un projectile est lancé à \\\\(v_0 = 12\\\\,\\\\mathrm{m/s}\\\\) sous \\\\(60^\\\\circ\\\\). Quelle est la hauteur maximale atteinte ? (\\\\(g = 9{,}8\\\\,\\\\mathrm{m/s^2}\\\\))",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La hauteur maximale est \\\\(H_{max} = \\\\frac{v_0^2 \\\\sin^2(\\\\theta)}{2g}\\\\). \\\\(\\\\sin(60^\\\\circ) = 0,866\\\\), donc \\\\(H_{max} = \\\\frac{144 \\\\times 0,75}{19,6} = \\\\frac{108}{19,6} \\\\approx 5,51\\\\,\\\\mathrm{m}\\\\).",
"answers": [
{
"answer_title": "5,5 m",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "3,8 m",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "7,1 m",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "4,1 m",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 8,
"question_title": "Un projectile est lancé à \\\\(v_0 = 10\\\\,\\\\mathrm{m/s}\\\\) sous \\\\(90^\\\\circ\\\\). Quelle est la portée maximale ? (\\\\(g = 9{,}8\\\\,\\\\mathrm{m/s^2}\\\\))",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "À \\\\(90^\\\\circ\\\\), \\\\(\\\\sin(180^\\\\circ) = 0\\\\), donc la portée est nulle : \\\\(R = 0\\\\,\\\\mathrm{m}\\\\).",
"answers": [
{
"answer_title": "0 m",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "10,2 m",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "5,1 m",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "20,4 m",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 9,
"question_title": "Un projectile est lancé à \\\\(v_0 = 16\\\\,\\\\mathrm{m/s}\\\\) sous \\\\(45^\\\\circ\\\\). Quelle est la hauteur maximale atteinte ? (\\\\(g = 9{,}8\\\\,\\\\mathrm{m/s^2}\\\\))",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La hauteur maximale est \\\\(H_{max} = \\\\frac{16^2 \\\\times (0,707)^2}{2 \\\\times 9,8} = \\\\frac{256 \\\\times 0,5}{19,6} = \\\\frac{128}{19,6} \\\\approx 6,53\\\\,\\\\mathrm{m}\\\\).",
"answers": [
{
"answer_title": "6,53 m",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "8,16 m",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "4,08 m",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "5,10 m",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 10,
"question_title": "Un projectile est lancé à \\\\(v_0 = 14\\\\,\\\\mathrm{m/s}\\\\) sous \\\\(30^\\\\circ\\\\). Quelle est la portée maximale ? (\\\\(g = 9{,}8\\\\,\\\\mathrm{m/s^2}\\\\))",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La portée maximale est \\\\(R = \\\\frac{14^2 \\\\times \\\\sin(60^\\\\circ)}{9,8} = \\\\frac{196 \\\\times 0,866}{9,8} = \\\\frac{169,736}{9,8} \\\\approx 17,3\\\\,\\\\mathrm{m}\\\\).",
"answers": [
{
"answer_title": "17,3 m",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "14,0 m",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "12,2 m",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "20,5 m",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 11,
"question_title": "Un projectile est lancé à \\\\(v_0 = 20\\\\,\\\\mathrm{m/s}\\\\) sous \\\\(60^\\\\circ\\\\). Quelle est la composante horizontale de la vitesse initiale ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La composante horizontale est \\\\(v_{0x} = v_0 \\\\cos(\\\\theta) = 20 \\\\times 0,5 = 10,0\\\\,\\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "10,0 m/s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "17,3 m/s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "20,0 m/s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "15,0 m/s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 12,
"question_title": "Un projectile est lancé à \\\\(v_0 = 25\\\\,\\\\mathrm{m/s}\\\\) sous \\\\(37^\\\\circ\\\\). Quelle est la composante verticale de la vitesse initiale ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La composante verticale est \\\\(v_{0y} = v_0 \\\\sin(\\\\theta) = 25 \\\\times 0,601 = 15,0\\\\,\\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "15,0 m/s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "20,0 m/s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "12,0 m/s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "18,0 m/s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 13,
"question_title": "Un projectile est lancé à \\\\(v_0 = 18\\\\,\\\\mathrm{m/s}\\\\) sous \\\\(90^\\\\circ\\\\). Quelle est la hauteur maximale atteinte ? (\\\\(g = 9{,}8\\\\,\\\\mathrm{m/s^2}\\\\))",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La hauteur maximale est \\\\(H_{max} = \\\\frac{18^2 \\\\times 1}{2 \\\\times 9,8} = \\\\frac{324}{19,6} \\\\approx 16,5\\\\,\\\\mathrm{m}\\\\).",
"answers": [
{
"answer_title": "16,5 m",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "9,0 m",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "8,3 m",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "12,5 m",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 14,
"question_title": "Un projectile est lancé à \\\\(v_0 = 10\\\\,\\\\mathrm{m/s}\\\\) sous \\\\(45^\\\\circ\\\\). Quelle est la composante horizontale de la vitesse initiale ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La composante horizontale est \\\\(v_{0x} = 10 \\\\times 0,707 = 7,07\\\\,\\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "7,07 m/s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "10,0 m/s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "5,00 m/s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "8,66 m/s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 15,
"question_title": "Un projectile est lancé à \\\\(v_0 = 16\\\\,\\\\mathrm{m/s}\\\\) sous \\\\(0^\\\\circ\\\\). Quelle est la composante verticale de la vitesse initiale ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "À \\\\(0^\\\\circ\\\\), \\\\(\\\\sin(0) = 0\\\\), donc la composante verticale est nulle.",
"answers": [
{
"answer_title": "0 m/s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "16,0 m/s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "8,0 m/s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "11,3 m/s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 16,
"question_title": "Un projectile est lancé à \\\\(v_0 = 22\\\\,\\\\mathrm{m/s}\\\\) sous \\\\(30^\\\\circ\\\\). Quelle est la composante horizontale de la vitesse initiale ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La composante horizontale est \\\\(v_{0x} = 22 \\\\times 0,866 = 19,1\\\\,\\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "19,1 m/s",
"is_correct": false,
"answer_order": 1
},
{
"answer_title": "11,0 m/s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "22,0 m/s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "19,1 m/s",
"is_correct": true,
"answer_order": 4
}
]
},
{
"question_order": 17,
"question_title": "Un projectile est lancé à \\\\(v_0 = 14\\\\,\\\\mathrm{m/s}\\\\) sous \\\\(60^\\\\circ\\\\). Quelle est la composante verticale de la vitesse initiale ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La composante verticale est \\\\(v_{0y} = 14 \\\\times 0,866 = 12,1\\\\,\\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "12,1 m/s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "7,0 m/s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "14,0 m/s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "8,7 m/s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 18,
"question_title": "Un projectile est lancé à \\\\(v_0 = 20\\\\,\\\\mathrm{m/s}\\\\) sous \\\\(45^\\\\circ\\\\). Quelle est la composante verticale de la vitesse initiale ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La composante verticale est \\\\(v_{0y} = 20 \\\\times 0,707 = 14,1\\\\,\\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "14,1 m/s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "10,0 m/s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "20,0 m/s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "12,5 m/s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 19,
"question_title": "Un projectile est lancé à \\\\(v_0 = 18\\\\,\\\\mathrm{m/s}\\\\) sous \\\\(0^\\\\circ\\\\). Quelle est la composante horizontale de la vitesse initiale ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "À \\\\(0^\\\\circ\\\\), \\\\(\\\\cos(0) = 1\\\\), donc la composante horizontale est \\\\(18,0\\\\,\\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "18,0 m/s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "0 m/s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "9,0 m/s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "12,7 m/s",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 20,
"question_title": "Un projectile est lancé à \\\\(v_0 = 15\\\\,\\\\mathrm{m/s}\\\\) sous \\\\(90^\\\\circ\\\\). Quelle est la composante horizontale de la vitesse initiale ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "À \\\\(90^\\\\circ\\\\), \\\\(\\\\cos(90^\\\\circ) = 0\\\\), donc la composante horizontale est nulle.",
"answers": [
{
"answer_title": "0 m/s",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "15,0 m/s",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "7,5 m/s",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "10,6 m/s",
"is_correct": false,
"answer_order": 4
}
]
}
]
}