// Numbas version: finer_feedback_settings
{"name": "SUVAT equations question 12", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["s", "a"], "name": "SUVAT equations question 12", "tags": [], "advice": "<p>We can model the plant pot as a particle moving in a straight line with a constant acceleration of $9.8ms^{-2}$, as it is accelerating under gravity. We will take the downward direction as the <em>positive</em> direction as the pot is falling <em>downwards</em>.</p>\n<p>a) We have $s=\\var{s}, a=\\var{a}$ and $u=0$ as we assume that the initial speed of the pot is zero. We want to find the time it hits the ground, $t$, therefore we can use the formula $s=ut+\\frac{1}{2}at^2$, with $u=0$,&nbsp;rearranged for $t$.</p>\n<p>Therefore \\begin{align} s &amp;= ut+\\frac{1}{2}at^2, \\\\<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &amp;= \\frac{1}{2}at^2, \\\\<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; t^2 &amp; = \\frac{2s}{a}, \\\\<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; t &amp; = \\sqrt{\\frac{2s}{a}}, \\\\<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&amp; = \\sqrt{\\frac{2\\times\\var{s}}{\\var{a}}},\\\\<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &amp; = \\var{precround(((2*s)/a)^(1/2),3)} \\mathrm{s}. \\end{align}&nbsp;<br/>The plant pot hits the ground after&nbsp;$\\var{precround(((2*s)/a)^(1/2),3)}$ seconds.&nbsp;</p>\n<p>b) We have $s=\\var{s}, u = 0$ and $a = 9.8$ and we want the speed with which the pot hits the ground, $v$. Therefore we can use the formula $v^2 = u^2 + 2as$.</p>\n<p>\\begin{align} v^2 &amp; = u^2 + 2as, \\\\<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&amp; = 0 + \\left(2 \\times \\var{a} \\times \\var{s}\\right), \\\\<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&amp; = \\var{precround(2*a*s,3)} \\mathrm{ms^{-1}} \\end{align}</p>\n<p>Therefore $v = \\sqrt{\\var{precround(2*a*s,3)}} = \\var{precround((2*a*s)^(1/2),3)} \\mathrm{ms^{-1}}$ so the pot hits the ground at $\\var{precround((2*a*s)^(1/2),3)} \\mathrm{ms^{-1}}$.</p>", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "<p>Find the time in $\\mathrm{s}$ (to 3d.p.) it takes for the pot to hit the ground.</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "(2*s/a)^(1/2)", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "(2*s/a)^(1/2)", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p>Find the speed in $\\mathrm{ms^{-1}}$ (to 3d.p.)&nbsp;with which the pot hits the ground.</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "(2*a*s)^(1/2)", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "(2*a*s)^(1/2)", "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>A plant pot falls off a window ledge which is $\\var{s} \\mathrm{m}$ above the garden floor. The acceleration due to gravity is $g= 9.8 \\mathrm{ms^{-2}}$</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "9.8", "templateType": "number", "group": "Ungrouped variables", "name": "a", "description": "<p>gravity acting downwards</p>"}, "s": {"definition": "random(0.5..4#0.25)", "templateType": "randrange", "group": "Ungrouped variables", "name": "s", "description": ""}}, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}]}]}], "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}]}