Ecrit par ✅ Quiz : Addition Relativiste Des Vitesses
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.
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{
"quiz_title": "Addition Relativiste Des Vitesses",
"quiz_slug": "07_addition_relativiste_des_vitesses_quiz",
"quiz_description": "Quiz Edu509 : Addition Relativiste Des Vitesses",
"quiz_settings": {
"time_limit": {
"time_value": 0,
"time_type": "minutes"
},
"hide_quiz_time_display": false,
"attempts_allowed": 0,
"passing_grade": 70,
"max_questions_for_answer": 0,
"questions_order": "rand",
"hide_question_number_overview": false,
"short_answer_characters_limit": 200
},
"questions": [
{
"question_order": 1,
"question_title": "Un vaisseau se déplace à \\\\(V = 2{,}00 \\\\times 10^7\\\\ \\\\mathrm{m/s}\\\\) par rapport à la Terre. Une sonde est lancée à \\\\(v' = 1{,}00 \\\\times 10^7\\\\ \\\\mathrm{m/s}\\\\) dans le même sens (par rapport au vaisseau). Quelle est la vitesse de la sonde par rapport à la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule relativiste : \\\\(v = \\\\frac{v' + V}{1 + \\\\frac{v'V}{c^2}}\\\\). En remplaçant les valeurs, on obtient \\\\(v = \\\\frac{3{,}00 \\\\times 10^7}{1{,}0022} \\\\approx 2{,}993 \\\\times 10^7\\\\ \\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "\\\\(2{,}993 \\\\times 10^7\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(3{,}00 \\\\times 10^7\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(2{,}00 \\\\times 10^7\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(1{,}00 \\\\times 10^7\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 2,
"question_title": "Un train se déplace à \\\\(V = 2{,}50 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) par rapport à la Terre. Un passager lance une balle vers l’avant à \\\\(v' = 1{,}50 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) (par rapport au train). Quelle est la vitesse de la balle par rapport à la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La formule donne \\\\(v = \\\\frac{1{,}50 \\\\times 10^8 + 2{,}50 \\\\times 10^8}{1 + \\\\frac{(1{,}50 \\\\times 10^8) \\\\times (2{,}50 \\\\times 10^8)}{(3{,}00 \\\\times 10^8)^2}} = \\\\frac{4{,}00 \\\\times 10^8}{1{,}4167} \\\\approx 2{,}825 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "\\\\(2{,}825 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(4{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(2{,}50 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(1{,}50 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 3,
"question_title": "Un vaisseau A se déplace à \\\\(V = 0{,}8c\\\\) par rapport à la Terre. Un vaisseau B se déplace à \\\\(v' = 0{,}6c\\\\) dans le même sens par rapport à A. Quelle est la vitesse de B par rapport à la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule : \\\\(v = \\\\frac{0{,}6c + 0{,}8c}{1 + 0{,}6 \\\\times 0{,}8} = \\\\frac{1{,}4c}{1{,}48} \\\\approx 0{,}946c\\\\).",
"answers": [
{
"answer_title": "\\\\(0{,}946c\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(1{,}4c\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(0{,}8c\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(0{,}6c\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 4,
"question_title": "Une navette spatiale se déplace à \\\\(V = 2{,}40 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) par rapport à la Terre. Un robot lance un projectile à \\\\(v' = 1{,}20 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) dans le même sens (par rapport à la navette). Quelle est la vitesse du projectile par rapport à la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On utilise la formule relativiste : \\\\(v = \\\\frac{1{,}20 \\\\times 10^8 + 2{,}40 \\\\times 10^8}{1 + \\\\frac{(1{,}20 \\\\times 10^8) \\\\times (2{,}40 \\\\times 10^8)}{(3{,}00 \\\\times 10^8)^2}} = \\\\frac{3{,}60 \\\\times 10^8}{1{,}32} \\\\approx 2{,}73 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "\\\\(2{,}73 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(3{,}60 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(2{,}40 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(1{,}20 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 5,
"question_title": "Un proton se déplace à \\\\(V = 2{,}80 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) par rapport à la Terre. Il émet un neutrino à \\\\(v' = 1{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) dans le même sens (par rapport au proton). Quelle est la vitesse du neutrino par rapport à la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule : \\\\(v = \\\\frac{1{,}00 \\\\times 10^8 + 2{,}80 \\\\times 10^8}{1 + \\\\frac{(1{,}00 \\\\times 10^8) \\\\times (2{,}80 \\\\times 10^8)}{(3{,}00 \\\\times 10^8)^2}} = \\\\frac{3{,}80 \\\\times 10^8}{1{,}3111} \\\\approx 2{,}90 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "\\\\(2{,}86 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(3{,}80 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(2{,}80 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(1{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 6,
"question_title": "Si \\\\(v' = 0{,}9c\\\\) et \\\\(V = 0{,}9c\\\\), quelle est la vitesse résultante \\\\(v\\\\) par rapport au référentiel fixe ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La formule donne \\\\(v = \\\\frac{0{,}9c + 0{,}9c}{1 + 0{,}9 \\\\times 0{,}9} = \\\\frac{1{,}8c}{1{,}81} \\\\approx 0{,}994c\\\\).",
"answers": [
{
"answer_title": "\\\\(0{,}994c\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(1{,}8c\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(0{,}9c\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(0{,}81c\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 7,
"question_title": "Un objet se déplace à \\\\(v' = 2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) dans un train allant à \\\\(V = 2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) (mêmes sens). Quelle est la vitesse de l’objet par rapport à la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule : \\\\(v = \\\\frac{2{,}00 \\\\times 10^8 + 2{,}00 \\\\times 10^8}{1 + \\\\frac{(2{,}00 \\\\times 10^8)^2}{(3{,}00 \\\\times 10^8)^2}} = \\\\frac{4{,}00 \\\\times 10^8}{1{,}4444} \\\\approx 2{,}77 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "\\\\(2{,}67 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(4{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(3{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 8,
"question_title": "Un photon se déplace à la vitesse \\\\(c\\\\) dans un référentiel mobile allant à \\\\(V = 0{,}5c\\\\) par rapport à la Terre. Quelle est la vitesse du photon par rapport à la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "La vitesse de la lumière reste \\\\(c\\\\) pour tous les observateurs, conformément au postulat d’Einstein.",
"answers": [
{
"answer_title": "\\\\(c\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(1{,}5c\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(0{,}5c\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(0{,}75c\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 9,
"question_title": "Si \\\\(v' = 0{,}5c\\\\) et \\\\(V = 0{,}5c\\\\), quelle est la vitesse résultante \\\\(v\\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule : \\\\(v = \\\\frac{0{,}5c + 0{,}5c}{1 + 0{,}5 \\\\times 0{,}5} = \\\\frac{1{,}0c}{1{,}25} = 0{,}8c\\\\).",
"answers": [
{
"answer_title": "\\\\(0{,}8c\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(1{,}0c\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(0{,}5c\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(0{,}25c\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 10,
"question_title": "Un vaisseau va à \\\\(V = 2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\). Un astronaute lance une balle à \\\\(v' = 1{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) dans le même sens. Quelle est la vitesse de la balle par rapport à la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule : \\\\(v = \\\\frac{1{,}00 \\\\times 10^8 + 2{,}00 \\\\times 10^8}{1 + \\\\frac{(1{,}00 \\\\times 10^8) \\\\times (2{,}00 \\\\times 10^8)}{(3{,}00 \\\\times 10^8)^2}} = \\\\frac{3{,}00 \\\\times 10^8}{1{,}2222} \\\\approx 2{,}454 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "\\\\(2{,}60 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(3{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(1{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 11,
"question_title": "Si \\\\(v' = 0{,}7c\\\\) et \\\\(V = 0{,}7c\\\\), quelle est la vitesse résultante \\\\(v\\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On calcule : \\\\(v = \\\\frac{0{,}7c + 0{,}7c}{1 + 0{,}7 \\\\times 0{,}7} = \\\\frac{1{,}4c}{1{,}49} \\\\approx 0{,}94c\\\\).",
"answers": [
{
"answer_title": "\\\\(0{,}94c\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(1{,}4c\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(0{,}7c\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(0{,}49c\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 12,
"question_title": "Un objet se déplace à \\\\(v' = 1{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) dans un référentiel mobile allant à \\\\(V = 2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) dans le sens opposé. Quelle est la vitesse de l’objet par rapport à la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On utilise la formule avec \\\\(V\\\\) négatif : \\\\(v = \\\\frac{1{,}00 \\\\times 10^8 - 2{,}00 \\\\times 10^8}{1 - \\\\frac{(1{,}00 \\\\times 10^8) \\\\times (2{,}00 \\\\times 10^8)}{(3{,}00 \\\\times 10^8)^2}} = \\\\frac{-1{,}00 \\\\times 10^8}{0{,}7778} \\\\approx -1{,}29 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "\\\\(1{,}29 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(3{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(1{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 13,
"question_title": "Si \\\\(v' = 0{,}3c\\\\) et \\\\(V = 0{,}4c\\\\), quelle est la vitesse résultante \\\\(v\\\\) ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule : \\\\(v = \\\\frac{0{,}3c + 0{,}4c}{1 + 0{,}3 \\\\times 0{,}4} = \\\\frac{0{,}7c}{1{,}12} \\\\approx 0{,}625c\\\\).",
"answers": [
{
"answer_title": "\\\\(0{,}58c\\\\)",
"is_correct": false,
"answer_order": 1
},
{
"answer_title": "\\\\(0{,}7c\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(0{,}12c\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(0{,}625c\\\\)",
"is_correct": true,
"answer_order": 4
}
]
},
{
"question_order": 14,
"question_title": "Un vaisseau va à \\\\(V = 2{,}50 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\). Un astronaute lance une balle à \\\\(v' = 2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) dans le même sens. Quelle est la vitesse de la balle par rapport à la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule : \\\\(v = \\\\frac{2{,}00 \\\\times 10^8 + 2{,}50 \\\\times 10^8}{1 + \\\\frac{(2{,}00 \\\\times 10^8) \\\\times (2{,}50 \\\\times 10^8)}{(3{,}00 \\\\times 10^8)^2}} = \\\\frac{4{,}50 \\\\times 10^8}{1{,}5556} \\\\approx 2{,}89 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "\\\\(2{,}89 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(4{,}50 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(2{,}50 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 15,
"question_title": "Un objet se déplace à \\\\(v' = 0{,}95c\\\\) dans un référentiel mobile allant à \\\\(V = 0{,}95c\\\\) dans le même sens. Quelle est la vitesse de l’objet par rapport au référentiel fixe ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule : \\\\(v = \\\\frac{0{,}95c + 0{,}95c}{1 + 0{,}95 \\\\times 0{,}95} = \\\\frac{1{,}9c}{1{,}9025} \\\\approx 0{,}9987c\\\\).",
"answers": [
{
"answer_title": "\\\\(0{,}9987c\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(1{,}9c\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(0{,}95c\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(0{,}9025c\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 16,
"question_title": "Un vaisseau va à \\\\(V = 1{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\). Un astronaute lance une balle à \\\\(v' = 1{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) dans le même sens. Quelle est la vitesse de la balle par rapport à la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule : \\\\(v = \\\\frac{1{,}00 \\\\times 10^8 + 1{,}00 \\\\times 10^8}{1 + \\\\frac{(1{,}00 \\\\times 10^8)^2}{(3{,}00 \\\\times 10^8)^2}} = \\\\frac{2{,}00 \\\\times 10^8}{1{,}1111} \\\\approx 1{,}80 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "\\\\(1{,}80 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(1{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(3{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 17,
"question_title": "Un vaisseau va à \\\\(V = 2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\). Un astronaute lance une balle à \\\\(v' = 1{,}50 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) dans le même sens. Quelle est la vitesse de la balle par rapport à la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule : \\\\(v = \\\\frac{1{,}50 \\\\times 10^8 + 2{,}00 \\\\times 10^8}{1 + \\\\frac{(1{,}50 \\\\times 10^8) \\\\times (2{,}00 \\\\times 10^8)}{(3{,}00 \\\\times 10^8)^2}} = \\\\frac{3{,}50 \\\\times 10^8}{1{,}3333} \\\\approx 2{,}63 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "\\\\(2{,}63 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(3{,}50 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(1{,}50 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 18,
"question_title": "Un vaisseau va à \\\\(V = 2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\). Un astronaute lance une balle à \\\\(v' = 2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) dans le sens opposé. Quelle est la vitesse de la balle par rapport à la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule avec \\\\(v'\\\\) négatif : \\\\(v = \\\\frac{-2{,}00 \\\\times 10^8 + 2{,}00 \\\\times 10^8}{1 - \\\\frac{(2{,}00 \\\\times 10^8)^2}{(3{,}00 \\\\times 10^8)^2}} = \\\\frac{0}{0{,}5556} = 0\\\\ \\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "\\\\(0\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(4{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(1{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 19,
"question_title": "Un vaisseau va à \\\\(V = 2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\). Un astronaute lance une balle à \\\\(v' = 1{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) dans le sens opposé. Quelle est la vitesse de la balle par rapport à la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "On applique la formule avec \\\\(v'\\\\) négatif : \\\\(v = \\\\frac{-1{,}00 \\\\times 10^8 + 2{,}00 \\\\times 10^8}{1 - \\\\frac{(1{,}00 \\\\times 10^8) \\\\times (2{,}00 \\\\times 10^8)}{(3{,}00 \\\\times 10^8)^2}} = \\\\frac{1{,}00 \\\\times 10^8}{0{,}7778} \\\\approx 1{,}29 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "\\\\(1{,}29 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(3{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(1{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 4
}
]
},
{
"question_order": 20,
"question_title": "Un vaisseau va à \\\\(V = 2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\). Un astronaute lance une balle à \\\\(v' = 1{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\) dans le même sens. Quelle est la vitesse classique (non relativiste) de la balle par rapport à la Terre ?",
"question_type": "single_choice",
"question_mark": 1,
"answer_required": true,
"randomize_question": false,
"show_question_mark": true,
"question_description": "",
"question_explanation": "En physique classique, on additionne simplement les vitesses : \\\\(v = v' + V = 1{,}00 \\\\times 10^8 + 2{,}00 \\\\times 10^8 = 3{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\).",
"answers": [
{
"answer_title": "\\\\(3{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": true,
"answer_order": 1
},
{
"answer_title": "\\\\(2{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 2
},
{
"answer_title": "\\\\(1{,}00 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 3
},
{
"answer_title": "\\\\(2{,}60 \\\\times 10^8\\\\ \\\\mathrm{m/s}\\\\)",
"is_correct": false,
"answer_order": 4
}
]
}
]
}