// Numbas version: exam_results_page_options
{"name": "Katy's copy of Rate of change", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "functions": {}, "name": "Katy's copy of Rate of change", "tags": [], "parts": [{"gaps": [{"strictPrecision": false, "mustBeReducedPC": 0, "correctAnswerFraction": false, "marks": "2", "mustBeReduced": false, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "showFeedbackIcon": true, "precisionPartialCredit": 0, "precisionType": "dp", "maxValue": "{a}-9.8*{b}", "type": "numberentry", "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "minValue": "{a}-9.8*{b}", "unitTests": [], "customMarkingAlgorithm": "", "precision": "1", "scripts": {}, "allowFractions": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}, {"strictPrecision": false, "mustBeReducedPC": 0, "correctAnswerFraction": false, "marks": "2", "mustBeReduced": false, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "showFeedbackIcon": true, "precisionPartialCredit": 0, "precisionType": "dp", "maxValue": "{a}^2/19.6", "type": "numberentry", "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "minValue": "{a}^2/19.6", "unitTests": [], "customMarkingAlgorithm": "", "precision": "1", "scripts": {}, "allowFractions": false, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}], "prompt": "<p>Calculate the speed of the missile (m/s) \\(\\var{b}\\) seconds after launch. Give your answer correct to one decimal place.</p>\n<p style=\"padding-left: 30px;\">\\(v = \\)&nbsp;[[0]]m/s</p>\n<p>What is the maximum height achieved by this missile?&nbsp;Give your answer correct to one decimal place.</p>\n<p style=\"padding-left: 30px;\">\\(h = \\)&nbsp;[[1]]m</p>", "variableReplacements": [], "unitTests": [], "sortAnswers": false, "marks": 0, "customMarkingAlgorithm": "", "type": "gapfill", "showFeedbackIcon": true, "scripts": {}, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}], "advice": "<p>\\(h=\\var{a}t-4.9t^2\\)</p>\n<p>Recall that speed is the rate of change of position with respect to time &nbsp; i.e. \\(v=\\frac{dh}{dt}\\)</p>\n<p style=\"padding-left: 30px;\">\\(v=\\frac{dh}{dt}=\\var{a}-2*4.9t\\)</p>\n<p>when \\(t=\\var{b}\\)</p>\n<p style=\"padding-left: 30px;\">\\(v=\\var{a}-2*4.9*\\var{b}\\)</p>\n<p style=\"padding-left: 30px;\">\\(v=\\simplify{{a}-9.8*{b}}m/s\\)</p>\n<p></p>\n<p>The missile will reach its maximum height when its speed = 0. &nbsp; i.e.&nbsp;\\(v=\\frac{dh}{dt}=\\var{a}-2*4.9t=0\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\var{a}=9.8t\\)</p>\n<p style=\"padding-left: 30px;\">\\(t=\\var{a}/9.8\\)</p>\n<p>The maximum height reached will occur when \\(t=\\simplify{{a}/9.8}\\)</p>\n<p style=\"padding-left: 30px;\">\\(h=\\var{a}*\\left(\\simplify{{a}/9.8}\\right)-4.9*\\left(\\simplify{{a}/9.8}\\right)^2\\)</p>\n<p style=\"padding-left: 30px;\">\\(h=\\simplify{{a}^2/19.6}\\)</p>\n<p style=\"padding-left: 30px;\">\\(h=\\simplify{{{a}/{19.6}^0.5}^2}\\)</p>\n<p></p>\n<p></p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Rate of change problem involving velocity &amp; acceleration</p>"}, "ungrouped_variables": ["a", "b"], "preamble": {"css": "", "js": ""}, "extensions": [], "variables": {"a": {"definition": "random(100..300#5)", "description": "", "name": "a", "group": "Ungrouped variables", "templateType": "randrange"}, "b": {"definition": "random(3..10#1)", "description": "", "name": "b", "group": "Ungrouped variables", "templateType": "randrange"}}, "rulesets": {}, "statement": "<p>A missile is launched straight up in the air. The height of the missile,&nbsp;\\(h\\)&nbsp;metres, above the ground \\(t\\) seconds after the launch button is pressed is given by:</p>\n<p style=\"padding-left: 30px;\">\\(h=\\var{a}t-4.9t^2\\)</p>", "variable_groups": [], "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Katy Dobson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/854/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Katy Dobson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/854/"}]}