// Numbas version: exam_results_page_options
{"name": "Vectors 2 with solution", "extensions": [], "custom_part_types": [], "resources": [["question-resources/image003.png", "/srv/numbas/media/question-resources/image003.png"], ["question-resources/hw1sol2.png", "/srv/numbas/media/question-resources/hw1sol2.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Vectors 2 with solution", "tags": [], "metadata": {"description": "<p>Resultant vector</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>A trolley that moves along a horizontal beam is acted upon by two forces as shown. Knowing that &nbsp;$\\alpha=\\var{a}^\\circ$,</p>\n<p><img src=\"resources/question-resources/image003.png\" width=\"285\" height=\"213\"/></p>", "advice": "<p style=\"text-align: left;\"><img src=\"resources/question-resources/hw1sol2.png\" width=\"242\" height=\"224\"/></p>\n<p style=\"text-align: left;\">Using the triangle rule and the rule of sines</p>\n<p style=\"text-align: left;\"><strong>(a)</strong></p>\n<p style=\"text-align: center;\">$\\dfrac{1600\\;\\text{N}}{\\sin \\alpha}=\\dfrac{P}{\\sin 75^\\circ}$</p>\n<p style=\"text-align: right;\">$P=\\var{P}\\;\\text{N}$&nbsp;\u25c0</p>\n<p style=\"text-align: left;\"><strong>(b)&nbsp;</strong></p>\n<p style=\"text-align: center;\">$\\alpha+\\beta+75^\\circ=180^\\circ$</p>\n<p style=\"text-align: center;\">$\\beta=180^\\circ-\\alpha-75^\\circ=\\var{b}^\\circ$</p>\n<p style=\"text-align: center;\">$\\dfrac{1600\\;\\text{N}}{\\sin \\alpha}=\\dfrac{R}{\\sin \\var{b}^\\circ}$</p>\n<p style=\"text-align: center;\">$R=(1600\\;\\text{N})\\dfrac{\\sin \\var{a}^\\circ}{\\sin \\var{b}^\\circ}$</p>\n<p style=\"text-align: right;\">$R=\\var{R}\\;\\text{N}$ \u25c0</p>", "rulesets": {}, "extensions": [], "variables": {"P": {"name": "P", "group": "Ungrouped variables", "definition": "precround(1600*sin(radians(75))/sin(radians(a)),1)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(5 .. 70#5)", "description": "", "templateType": "randrange"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "180-75-a", "description": "", "templateType": "anything"}, "R": {"name": "R", "group": "Ungrouped variables", "definition": "precround(sqrt({P}^2+1600^2-2*{P}*1600*cos(radians(180-75-{a}))),1)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "P", "R", "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 by trigonometry the magnitude of the force $\\mathbf{P}$&nbsp;(in N) so that the resultant force exerted on the trolley is vertical.</p>", "minValue": "{P}-1", "maxValue": "{P}+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>Determine the corresponding magnitude of the resultant (in N).</p>", "minValue": "{R}-1", "maxValue": "{R}+1", "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/"}]}