// Numbas version: exam_results_page_options
{"name": "Diving board", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Diving board", "tags": [], "metadata": {"description": "<p>Student needs to solve a quadratic equation to calculate time taken for a diver to hit the water after diving from a diving board. Height of the board and initial upward velocity of the diver are randomly generated values. student needs to know that surface of the water is height 0, and only positive root of quadratic has physical meaning. Question is set to always give one positieve and one negative root.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>We are given that the divers height above the water at time \\(t\\) is given by \\[h(t)=\\simplify{-4.9t^2+{velocity}t+{height}} \\text{ metres.}\\]</p>\n<p>Since the surface of the water will be at height \\(h(t)=0\\) we need to solve \\[\\simplify{-4.9t^2+{velocity}t+{height}}=0.\\]</p>\n<p>To do this we use the quadratic formula giving us</p>\n<p>\\begin{align}t&amp;=\\frac{-\\var{velocity}\\pm\\sqrt{\\var{velocity}^2+4\\times\\var{height}\\times 4.9}}{-2\\times 4.9}\\\\&amp;=\\frac{-\\var{velocity}\\pm\\sqrt{\\var{velocity^2+4*height*4.9}}}{-9.8}\\\\&amp;\\approx \\var{time}\\text{ or }\\var{negRoot}\\end{align}</p>\n<p>Since time needs to be a positive quantity for the solution to make sense we can dismiss the negative root and conclude that it takes \\(\\var{time}\\) seconds for the diver to hit the water.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"height": {"name": "height", "group": "Ungrouped variables", "definition": "random(1.5..10 #0.5)", "description": "<p>height of diving board above the water</p>", "templateType": "anything", "can_override": false}, "velocity": {"name": "velocity", "group": "Ungrouped variables", "definition": "random(1.5..5 #0.1)", "description": "<p>initial vertical velocity of diver (positive is taken as upward direction).</p>", "templateType": "anything", "can_override": false}, "time": {"name": "time", "group": "Ungrouped variables", "definition": "precround((-velocity-sqrt(velocity^2+19.6*height))/-9.8,2)", "description": "<p>Time talen for diver to hit the water.</p>", "templateType": "anything", "can_override": false}, "negRoot": {"name": "negRoot", "group": "Ungrouped variables", "definition": "precround((-velocity+sqrt(velocity^2+19.6*height))/-9.8,2)", "description": "<p>negative root of quadratic equation.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["height", "velocity", "time", "negRoot"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A diver jumps off a diving board \\(\\var{height}\\) metres above the water with an initial vertical velocity of \\(\\var{velocity}\\) m/s. The diver's height above the water is given by</p>\n<p>\\[h(t)=\\simplify{-4.9t^2+{velocity}t+{height}} \\text{ metres}\\]</p>\n<p>How long does it take for the diver to hit the water? (Give your answer correct to 2 decimal places)</p>\n<p>It takes [[0]] seconds to hit the water. Show full working on your handwritten notes.</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{time}", "maxValue": "{time}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}]}