// Numbas version: exam_results_page_options
{"name": "Vectors 1 with solutions", "extensions": [], "custom_part_types": [], "resources": [["question-resources/image001.png", "/srv/numbas/media/question-resources/image001.png"], ["question-resources/hw1sol1.png", "/srv/numbas/media/question-resources/hw1sol1.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Vectors 1 with solutions", "tags": [], "metadata": {"description": "<p>Resultant force</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<div class=\"page\" title=\"Page 2\">\n<div class=\"section\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<p>Two forces are applied as shown to a hook support. Knowing that the magnitude of $\\mathbf{P}$&nbsp;is {P}N,&nbsp;</p>\n<p><img src=\"resources/question-resources/image001.png\"/></p>\n</div>\n</div>\n</div>\n</div>", "advice": "<p><img src=\"resources/question-resources/hw1sol1.png\" width=\"193\" height=\"107\"/></p>\n<p>Using the triangle rule and law of sines:</p>\n<p><strong>(a)</strong> Solve</p>\n<p style=\"text-align: center;\">$\\dfrac{\\sin \\alpha}{50\\,\\text{N}}=\\dfrac{\\sin 25^\\circ}{P}$</p>\n<p style=\"text-align: center;\">$\\sin \\alpha=\\sin 25^\\circ \\dfrac{50\\,\\text{N}}{\\var{P}}=\\var{sina}$</p>\n<p style=\"text-align: center;\">$\\alpha=\\arcsin(\\var{sina})=\\var{a}^\\circ$</p>\n<p style=\"text-align: right;\">$\\alpha=\\var{a}^\\circ\\,\\,$ &nbsp;\u25c0</p>\n<p style=\"text-align: left;\"><strong>(b)</strong>&nbsp;</p>\n<p style=\"text-align: center;\">$\\alpha+\\beta+25^\\circ=180^\\circ$</p>\n<p style=\"padding-left: 30px; text-align: center;\">$\\beta=180^\\circ-25^\\circ-\\var{a}^\\circ=\\var{b}^\\circ$</p>\n<p style=\"padding-left: 30px; text-align: center;\">$\\dfrac{R}{\\sin \\var{b}^\\circ}=\\dfrac{\\var{P}\\,\\text{N}}{\\sin 25^\\circ}$</p>\n<p style=\"text-align: right;\">$R=\\var{R}\\,\\text{N}$ &nbsp; \u25c0</p>", "rulesets": {}, "extensions": [], "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "180-25-a", "description": "", "templateType": "anything"}, "sina": {"name": "sina", "group": "Ungrouped variables", "definition": "precround(50*sin(25*pi/180)/{P},4)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "precround(degrees(arcsin(50*sin(25*pi/180)/{P})),2)", "description": "", "templateType": "anything"}, "R": {"name": "R", "group": "Ungrouped variables", "definition": "precround(sqrt({P}^2+50^2-2*{P}*50*cos(radians(180-25-{a}))),2)", "description": "", "templateType": "anything"}, "P": {"name": "P", "group": "Ungrouped variables", "definition": "random(22 .. 80#1)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["P", "a", "R", "sina", "b"], "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 required angle <i>$\\alpha$</i>&nbsp;(in degrees) if the resultant $\\mathbf{R}$&nbsp;of the two forces applied to the support is to be horizontal.</p>", "minValue": "{a}-0.25", "maxValue": "{a}+0.25", "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>Determine the corresponding magnitude of $\\mathbf{R}$&nbsp;(in N)</p>", "minValue": "{R}-0.5", "maxValue": "{R}+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/"}]}