// Numbas version: finer_feedback_settings
{"name": "Dekomponering i polare koordinater", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Dekomponering i polare koordinater", "tags": [], "metadata": {"description": "<p>&Oslash;velse i &aring; g&aring; fra kartesiske til polare basisvektorer.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "<p>Posisjonen har ingen komponent i \\(\\hat{\\phi}\\) retningen fordi \\(\\vec{r}\\) og \\(\\hat{r}\\) er parallell. Komponenten i \\(\\hat{r}\\)-retningen er avstand fra origo, s&aring; \\(\\vec{r}=\\sqrt{\\var{x}^2+\\var{y}^2}\\hat{r}\\). </p>\n<p></p>\n<p>Hastigheten kan skrives \\(\\vec{v}=v_r\\hat{r}+v_\\phi\\hat{\\phi}\\) der \\(v_r\\) og \\(v_\\phi\\) er de ukjente variablene. For &aring; finne \\(v_r\\)</p>", "rulesets": {}, "extensions": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything"}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(-4..4 except 0)", "description": "", "templateType": "anything"}, "vx": {"name": "vx", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything"}, "vy": {"name": "vy", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything"}, "r": {"name": "r", "group": "Ungrouped variables", "definition": "vector(x,y,0)/sqrt(x^2+y^2)", "description": "", "templateType": "anything"}, "phi": {"name": "phi", "group": "Ungrouped variables", "definition": "cross(r,vector(0,0,-1))", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "y", "vx", "vy", "r", "phi"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Posisjon", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>En partikkel har en posisjon gitt ved \\(\\vec{r}=\\var{x}\\hat{x}+\\var{y}\\hat{y}\\).</p>\n<p>Hva er posisjonen gitt i polare koordinater?</p>\n<p></p>\n<p>\\(\\vec{r}=\\)[[0]]\\(\\hat{r}+\\)[[1]]\\(\\hat{\\phi}\\)</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "1", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "sqrt({x}^2+{y}^2)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "2", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "0", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Hastighet", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Partikkelen har en hastighet gitt ved \\(\\vec{v}=\\var{vx}\\hat{x}+\\var{vy}\\hat{y}\\).</p>\n<p>Hva er hastigheten gitt i polare koordinater?</p>\n<p></p>\n<p>\\(\\vec{v}=\\)[[0]]\\(\\hat{r}+\\)[[1]]\\(\\hat{\\phi}\\)</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "vr", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "dot({r},vector({vx},{vy},0))", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": "0.01", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "vphi", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "dot(vector({vx},{vy},0),{phi})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": "0.01", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "B\u00f8rge Irgens", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/10762/"}]}]}], "contributors": [{"name": "B\u00f8rge Irgens", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/10762/"}]}