// Numbas version: finer_feedback_settings
{"name": "Je laat een bal van een toren vallen", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Je laat een bal van een toren vallen", "tags": [], "metadata": {"description": "<p>Hoogte, valtijd en gemiddelde snelheid berekenen.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Je laat een bal van een toren vallen. De hoogte $h$ van de bal ten opzichte van de grond (in meter) na $t$ seconden wordt beschreven door de functie met voorschrift $h(t)=-4,9t&sup2;+\\var{hoogte}$.</p>", "advice": "<p>De hoogte is de constante term uit de vergelijking (op $t=0$ bevindt de bal zich bovenaan de toren), dus {hoogte} m.</p>\n<p>De valtijd bedraagt $h = 0 &lt;=&gt; 0 = -4,9t&sup2; + \\var{hoogte} &lt;=&gt; t&sup2; = \\frac{\\var{hoogte}}{4,9} &lt;=&gt; t = \\sqrt{\\frac{\\var{hoogte}}{4,9}}=\\var{formatnumber(precround(grond,1),\"plain-eu\")}$ s.</p>\n<p>De gemiddelde snelheid is het differentiequoti&euml;nt over het interval $[0; \\var{tijd}]$.</p>\n<p>$\\frac{f(\\var{tijd})-f(0)}{\\var{tijd}-0}=\\frac{-4,9 \\cdot \\var{tijd}&sup2;+\\var{hoogte}-\\var{hoogte}}{\\var{tijd}}=-4,9 \\cdot \\var{tijd} = \\var{formatnumber(precround(snelheid,2),\"plain-eu\")}$$\\frac{m}{s}$</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"hoogte": {"name": "hoogte", "group": "Ungrouped variables", "definition": "random(10 .. 99#1)", "description": "", "templateType": "randrange", "can_override": false}, "tijd": {"name": "tijd", "group": "Ungrouped variables", "definition": "random(0.3 .. 1#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "grond": {"name": "grond", "group": "Ungrouped variables", "definition": "sqrt(hoogte/4.9)", "description": "", "templateType": "anything", "can_override": false}, "snelheid": {"name": "snelheid", "group": "Ungrouped variables", "definition": "(-4.9*tijd)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["hoogte", "tijd", "grond", "snelheid"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Hoe hoog is de toren?</p>\n<p>[[0]] m</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "hoogte", "maxValue": "hoogte", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Na hoeveel seconden raakt de steen de grond?</p>\n<p>[[0]] s</p>\n<p>Geef je antwoord op 1 decimaal nauwkeurig.</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "grond", "maxValue": "grond", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Wat is de gemiddelde snelheid van de bal in de eerste {formatnumber(tijd,\"plain-eu\")} seconden van de val?</p>\n<p>Geef je antwoord op twee decimalen nauwkeurig.</p>\n<p>De gemiddelde snelheid van de bal in de eerste {formatnumber(tijd,\"plain-eu\")} seconden van de val bedraagt [[0]] $\\frac{m}{s}$.</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "snelheid", "maxValue": "snelheid", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en", "plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Hans Denayer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18121/"}]}]}], "contributors": [{"name": "Hans Denayer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18121/"}]}