// Numbas version: finer_feedback_settings
{"name": "Jinhua'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": [{"functions": {}, "ungrouped_variables": ["cts", "ct"], "name": "Jinhua's copy of Differentiation 17 - Applications", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>From the steps provided, we found that at the stationary point of the projectile parabola:</p>\n<p>$\\frac{dy}{dx}=0$ &nbsp; &nbsp;and &nbsp; &nbsp;$t=\\simplify{{ct}/{2*{cts}}}$</p>\n<p>To find the maximum height, the value for $t$ at the stationary point is substituted back into the original equation:</p>\n<p>$y=\\var{ct}t-\\var{cts}t^2=\\var{ct}\\left(\\simplify{{ct}/{2*{cts}}}\\right)-\\var{cts}\\left(\\simplify{{ct}/{2*{cts}}}\\right)^2$</p>", "rulesets": {}, "parts": [{"stepsPenalty": "2", "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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}, {"vsetrangepoints": 5, "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>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{ct}-2{cts}t", "marks": "0", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"prompt": "<p>Therefore, $t=$</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "{ct}/(2{cts})", "minValue": "{ct}/(2{cts})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": "0", "type": "numberentry", "showPrecisionHint": false}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{ct}-2{cts}t", "marks": "1", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": true, "variableReplacements": [], "maxValue": "{ct}({ct}/(2{cts}))-{cts}({ct}/(2{cts}))^2", "strictPrecision": false, "minValue": "{ct}({ct}/(2{cts}))-{cts}({ct}/(2{cts}))^2", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": "50", "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "0", "scripts": {}, "marks": "3", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "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>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"cts": {"definition": "random(3..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "cts", "description": "<p>coeff of t^2</p>"}, "ct": {"definition": "siground(random(30..90),1)", "templateType": "anything", "group": "Ungrouped variables", "name": "ct", "description": "<p>coeff of t</p>"}}, "metadata": {"description": "<p>Real life problems with differentiation</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}]}], "contributors": [{"name": "", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}