// Numbas version: finer_feedback_settings
{"name": "Harry'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": [{"question_groups": [{"pickQuestions": 0, "name": "", "pickingStrategy": "all-ordered", "questions": []}], "variablesTest": {"maxRuns": 100, "condition": ""}, "name": "Harry's copy of Differentiation 17 - Applications", "parts": [{"type": "gapfill", "stepsPenalty": "2", "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "gaps": [{"showpreview": true, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "variableReplacements": [], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "showCorrectAnswer": true, "type": "jme", "marks": "1", "checkingtype": "absdiff", "scripts": {}, "answer": "{ct}-2{cts}t", "vsetrange": [0, 1], "checkvariablenames": false, "answersimplification": "all"}, {"allowFractions": true, "variableReplacementStrategy": "originalfirst", "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "precision": "0", "showCorrectAnswer": true, "type": "numberentry", "precisionType": "dp", "showPrecisionHint": false, "correctAnswerFraction": false, "precisionPartialCredit": "50", "minValue": "{ct}({ct}/(2{cts}))-{cts}({ct}/(2{cts}))^2", "strictPrecision": false, "scripts": {}, "maxValue": "{ct}({ct}/(2{cts}))-{cts}({ct}/(2{cts}))^2", "marks": "3"}], "prompt": "<p>$y=\\var{ct}t-\\var{cts}t^2$</p>\n<p>Firstly, differentiate.</p>\n<p>$\\frac{dy}{dx}=$&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>", "showCorrectAnswer": true, "steps": [{"type": "information", "variableReplacementStrategy": "originalfirst", "marks": 0, "variableReplacements": [], "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>", "showCorrectAnswer": true, "scripts": {}}, {"showpreview": true, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "variableReplacements": [], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "showCorrectAnswer": true, "type": "jme", "marks": "0", "prompt": "<p>The maximum height will be at the stationary point.</p>\n<p>The stationary point can be found by equating $\\frac{dy}{dx}$ to $0$.</p>\n<p>$\\frac{dy}{dx}=0=$</p>", "checkingtype": "absdiff", "scripts": {}, "answer": "{ct}-2{cts}t", "vsetrange": [0, 1], "checkvariablenames": false, "answersimplification": "all"}, {"allowFractions": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "type": "numberentry", "showPrecisionHint": false, "correctAnswerFraction": true, "marks": "0", "prompt": "<p>Therefore, $t=$</p>", "scripts": {}, "maxValue": "{ct}/(2{cts})", "minValue": "{ct}/(2{cts})"}], "scripts": {}}], "rulesets": {}, "tags": [], "ungrouped_variables": ["cts", "ct"], "variable_groups": [], "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>", "functions": {}, "type": "question", "showQuestionGroupNames": false, "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Real life problems with differentiation</p>"}, "variables": {"ct": {"group": "Ungrouped variables", "definition": "siground(random(30..90),1)", "name": "ct", "templateType": "anything", "description": "<p>coeff of t</p>"}, "cts": {"group": "Ungrouped variables", "definition": "random(3..9)", "name": "cts", "templateType": "anything", "description": "<p>coeff of t^2</p>"}}, "preamble": {"js": "", "css": ""}, "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>", "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}]}], "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}