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{"name": " Vectors 4 with solution", "extensions": [], "custom_part_types": [], "resources": [["question-resources/image008.png", "/srv/numbas/media/question-resources/image008.png"], ["question-resources/hw1sol4.png", "/srv/numbas/media/question-resources/hw1sol4.png"], ["question-resources/hw1sol4b.png", "/srv/numbas/media/question-resources/hw1sol4b.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": " Vectors 4 with solution", "tags": [], "metadata": {"description": "<p>Resultant force</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>The cable stays <i>AB</i> and <i>AD</i> help support pole <i>AC</i>. Knowing that the tension is {tAB}N in <i>AB</i> and {tAD}N in <i>AD,</i></p>\n<p><i><img src=\"resources/question-resources/image008.png\" width=\"400\" height=\"292\"/></i></p>\n<p><i></i></p>", "advice": "<p style=\"padding-left: 30px; text-align: left;\"><img src=\"resources/question-resources/hw1sol4.png\" width=\"321\" height=\"238\"/></p>\n<p style=\"text-align: center;\">$\\tan \\alpha=\\frac{8}{10}\\quad\\Rightarrow\\quad \\alpha=\\var{gammaAB}^\\circ$&nbsp;</p>\n<p style=\"text-align: center;\">$\\tan \\beta=\\frac{6}{10}\\quad\\Rightarrow\\quad \\beta=\\var{gammaAD}^\\circ$&nbsp;</p>\n<p style=\"text-align: left;\"><strong>(a)&nbsp;</strong>Using the triangle rule</p>\n<p style=\"padding-left: 30px; text-align: left;\"><img src=\"resources/question-resources/hw1sol4b.png\" width=\"180\" height=\"254\"/></p>\n<p style=\"padding-left: 30px; text-align: center;\">$\\alpha+\\beta+\\psi=180^\\circ$</p>\n<p style=\"padding-left: 30px; text-align: center;\">$\\psi=180^\\circ-\\var{gammaAB}^\\circ-\\var{gammaAD}^\\circ=110.38^\\circ$</p>\n<p style=\"padding-left: 30px; text-align: left;\">Using the rule of cosines</p>\n<p style=\"padding-left: 30px; text-align: center;\">$R^2=T_{AB}^2+T_{AD}^2-2T_{AB}T_{AD}\\cos\\psi$</p>\n<p style=\"padding-left: 30px; text-align: center;\">$R^2=\\var{tAB}^2+\\var{tAD}^2-2(\\var{tAB})(\\var{tAD})\\cos&nbsp;110.38^\\circ$</p>\n<p></p>\n<p style=\"text-align: right;\">$R=\\var{R}\\,\\text{N}$ \u25c0</p>\n<p style=\"text-align: left;\"><strong>(b)</strong> Use the rule of sines&nbsp;</p>\n<p style=\"text-align: center;\">$\\dfrac{\\sin \\gamma}{T_{AD}}=\\dfrac{\\sin \\psi}{R}$</p>\n<p style=\"text-align: center;\">$\\dfrac{\\sin \\gamma}{\\var{tAD}\\,\\text{N}}=\\dfrac{\\sin 110.38^\\circ}{\\var{R}\\,\\text{N}}$</p>\n<p style=\"text-align: right;\">$\\gamma=\\var{a}^\\circ$&nbsp;\u25c0</p>", "rulesets": {}, "extensions": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "precround(degrees(arcsin({tAD}*sin(radians(180-gammaAB-gammaAD))/{R})),2)", "description": "", "templateType": "anything"}, "gammaAD": {"name": "gammaAD", "group": "Ungrouped variables", "definition": "precround(degrees(arctan(6/10)),2)", "description": "", "templateType": "anything"}, "R": {"name": "R", "group": "Ungrouped variables", "definition": "precround(sqrt({tAB}^2+{tAD}^2-2*{tAB}*{tAD}*cos(radians(180-gammaAB-gammaAD))),1)", "description": "", "templateType": "anything"}, "gammaAB": {"name": "gammaAB", "group": "Ungrouped variables", "definition": "precround(degrees(arctan(8/10)),2)", "description": "", "templateType": "anything"}, "tAB": {"name": "tAB", "group": "Ungrouped variables", "definition": "random(40 .. 160#2)", "description": "", "templateType": "randrange"}, "tAD": {"name": "tAD", "group": "Ungrouped variables", "definition": "random(40 .. 160#2)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["tAB", "tAD", "R", "gammaAB", "gammaAD", "a"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "prompt": "<p>Determine the magnitude of the resultant (in N) of the forces exerted by the stays at <i>A</i> using the triangle rule.</p>", "minValue": "{R}-1", "maxValue": "{R}+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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, "prompt": "<p>What is the direction of the resultant force&nbsp;(measured from the stay <em>AB</em> in degrees) ?</p>", "minValue": "{a}-0.5", "maxValue": "{a}+0.5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Vladimir Vingoradov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1862/"}]}]}], "contributors": [{"name": "Vladimir Vingoradov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1862/"}]}