// Numbas version: exam_results_page_options
{"name": "Rate of change", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": ["a", "b"], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Rate of change problem involving velocity &amp; acceleration</p>"}, "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>", "extensions": [], "rulesets": {}, "variable_groups": [], "functions": {}, "preamble": {"css": "", "js": ""}, "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>", "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"b": {"templateType": "randrange", "description": "", "definition": "random(3..10#1)", "name": "b", "group": "Ungrouped variables"}, "a": {"templateType": "randrange", "description": "", "definition": "random(100..300#5)", "name": "a", "group": "Ungrouped variables"}}, "tags": [], "parts": [{"showCorrectAnswer": true, "type": "gapfill", "variableReplacements": [], "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>", "gaps": [{"precisionPartialCredit": 0, "variableReplacements": [], "precisionType": "dp", "correctAnswerFraction": false, "showPrecisionHint": false, "strictPrecision": false, "allowFractions": false, "scripts": {}, "minValue": "{a}-9.8*{b}", "showCorrectAnswer": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "precision": "1", "marks": 1, "maxValue": "{a}-9.8*{b}", "precisionMessage": "You have not given your answer to the correct precision."}, {"precisionPartialCredit": 0, "variableReplacements": [], "precisionType": "dp", "correctAnswerFraction": false, "showPrecisionHint": false, "strictPrecision": false, "allowFractions": false, "scripts": {}, "minValue": "{a}^2/19.6", "showCorrectAnswer": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "precision": "1", "marks": 1, "maxValue": "{a}^2/19.6", "precisionMessage": "You have not given your answer to the correct precision."}], "marks": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst"}], "name": "Rate of change", "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}