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{"name": "Blathnaid's copy of Vicky's copy of Differentiation 17 - Applications", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "<p>Real life problems with differentiation</p>", "licence": "Creative Commons Attribution 4.0 International"}, "name": "Blathnaid's copy of Vicky's copy of Differentiation 17 - Applications", "rulesets": {}, "parts": [{"stepsPenalty": "2", "type": "gapfill", "showCorrectAnswer": true, "marks": 0, "prompt": "<p>$y=\\var{ct}t-\\var{cts}t^2$</p>\n<p>Firstly, differentiate.</p>\n<p>$\\frac{dy}{dt}=$&nbsp;[[0]]</p>\n<p>Now use this result and your knowledge of differentiation to find the maximum height of the missile, rounding to the nearest whole number.</p>\n<p>$y=$&nbsp;[[1]]</p>\n<p></p>", "variableReplacements": [], "steps": [{"type": "information", "variableReplacements": [], "showCorrectAnswer": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "prompt": "<p>The missile will follow a parabolic curve when height is plotted against time.</p>\n<p>It takes the same amount of time to reach its maximum as it does to fall back down.</p>", "scripts": {}}, {"checkingaccuracy": 0.001, "showCorrectAnswer": true, "vsetrange": [0, 1], "marks": "0", "variableReplacementStrategy": "originalfirst", "prompt": "<p>The maximum height will be at the stationary point.</p>\n<p>The stationary point can be found by equating $\\frac{dy}{dt}$ to $0$.</p>\n<p>$\\frac{dy}{dt}=0=$</p>", "expectedvariablenames": [], "vsetrangepoints": 5, "type": "jme", "variableReplacements": [], "checkingtype": "absdiff", "showpreview": true, "answersimplification": "all", "answer": "{ct}-2{cts}t", "checkvariablenames": false, "scripts": {}}, {"type": "numberentry", "variableReplacements": [], "showCorrectAnswer": true, "allowFractions": true, "marks": "0", "maxValue": "{ct}/(2{cts})", "prompt": "<p>Therefore, $t=$</p>", "minValue": "{ct}/(2{cts})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "scripts": {}}], "gaps": [{"checkingaccuracy": 0.001, "showCorrectAnswer": true, "vsetrange": [0, 1], "marks": "1", "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "vsetrangepoints": 5, "type": "jme", "answer": "{ct}-2{cts}t", "checkingtype": "absdiff", "showpreview": true, "answersimplification": "all", "variableReplacements": [], "checkvariablenames": false, "scripts": {}}, {"precisionType": "dp", "precisionPartialCredit": "50", "marks": "3", "variableReplacementStrategy": "originalfirst", "minValue": "{ct}({ct}/(2{cts}))-{cts}({ct}/(2{cts}))^2", "precision": "0", "strictPrecision": false, "type": "numberentry", "maxValue": "{ct}({ct}/(2{cts}))-{cts}({ct}/(2{cts}))^2", "showCorrectAnswer": true, "allowFractions": true, "showPrecisionHint": false, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "scripts": {}, "correctAnswerFraction": false}], "scripts": {}, "variableReplacementStrategy": "originalfirst"}], "variable_groups": [], "variables": {"ct": {"definition": "siground(random(30..90),1)", "description": "<p>coeff of t</p>", "templateType": "anything", "group": "Ungrouped variables", "name": "ct"}, "cts": {"definition": "random(3..9)", "description": "<p>coeff of t^2</p>", "templateType": "anything", "group": "Ungrouped variables", "name": "cts"}}, "ungrouped_variables": ["cts", "ct"], "type": "question", "tags": [], "statement": "<p>An unpowered missile is launched vertically from the ground.</p>\n<p>At a time $t$ seconds after the instant of projection, its height, $y$ metres, above the ground is given by the formula</p>\n<p>\\[ y=\\var{ct}t-\\var{cts}t^2. \\]</p>\n<p><strong>Calculate the maximum height reached by the missile.</strong></p>", "showQuestionGroupNames": false, "extensions": [], "advice": "<p>This section draws on the skills learnt the previous parts of the&nbsp;<em>'Differentiation'</em> series of questions, and some logical thinking about the physics of the problem.</p>\n<p>The steps within the part walk through the&nbsp;process.</p>", "functions": {}, "preamble": {"js": "", "css": ""}, "question_groups": [{"questions": [], "name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0}], "variablesTest": {"maxRuns": 100, "condition": ""}, "contributors": [{"name": "Blathnaid Sheridan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/447/"}]}]}], "contributors": [{"name": "Blathnaid Sheridan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/447/"}]}