// Numbas version: exam_results_page_options
{"name": "Vectors 3 with solution", "extensions": [], "custom_part_types": [], "resources": [["question-resources/image003_kvrzVXi.png", "/srv/numbas/media/question-resources/image003_kvrzVXi.png"], ["question-resources/hw1sol2_1vcEBkn.png", "/srv/numbas/media/question-resources/hw1sol2_1vcEBkn.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Vectors 3 with solution", "tags": [], "metadata": {"description": "<p>Resultant force</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.</p>\n<p><img src=\"resources/question-resources/image003_kvrzVXi.png\" width=\"282\" height=\"211\"/></p>", "advice": "<p style=\"text-align: center;\"><img src=\"resources/question-resources/hw1sol2_1vcEBkn.png\" width=\"238\" height=\"220\"/></p>\n<p><strong>(a) </strong>Use the rule of cosines:</p>\n<p style=\"text-align: center;\">$P^2=(1600\\,\\text{N})^2+R^2-2(1600\\,\\text{N})R \\cos 75^\\circ$</p>\n<p style=\"text-align: center;\">$P=\\sqrt{1600^2+\\var{R}^2-2\\times&nbsp;1600\\times\\var{R}\\cos 75^\\circ}$</p>\n<p style=\"text-align: right;\">$P=\\var{P}\\,\\text{N}$&nbsp;\u25c0</p>\n<p style=\"text-align: left;\"><strong>(b) </strong>Use the rule of sines:</p>\n<p style=\"text-align: center;\">$\\dfrac{\\sin \\alpha}{1600N}=\\dfrac{\\sin 75^\\circ}{P}$</p>\n<p style=\"text-align: center;\">$\\sin \\alpha=\\sin 75^\\circ&nbsp;\\dfrac{1600\\,\\text{N}}{\\var{P}\\,\\text{N}}$</p>\n<p style=\"text-align: right;\">$\\alpha=\\var{a}^\\circ$&nbsp;\u25c0</p>", "rulesets": {}, "extensions": [], "variables": {"P": {"name": "P", "group": "Ungrouped variables", "definition": "precround(sqrt(1600^2+{R}^2-2*1600*{R}*cos(radians(75))),1)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "precround(degrees(arcsin(sin(radians(75))*1600/{P})),2)", "description": "", "templateType": "anything"}, "R": {"name": "R", "group": "Ungrouped variables", "definition": "random(1000 .. 3000#100)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["R", "P", "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 by trigonometry the magnitude of the force $\\mathbf{P}$&nbsp;(in N) so that the resultant is a vertical force of {R}&nbsp;N.&nbsp;</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&nbsp;direction of the force $\\mathbf{P}$&nbsp;(angle $\\alpha$ 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/"}]}