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{"name": "Vectors 5 with solution", "extensions": [], "custom_part_types": [], "resources": [["question-resources/image010.png", "/srv/numbas/media/question-resources/image010.png"], ["question-resources/hw1sol5.png", "/srv/numbas/media/question-resources/hw1sol5.png"], ["question-resources/Fig1-5_PhexlpW.png", "/srv/numbas/media/question-resources/Fig1-5_PhexlpW.png"], ["question-resources/hw1sol5_i9cD3k9.png", "/srv/numbas/media/question-resources/hw1sol5_i9cD3k9.png"], ["question-resources/hw1sol5_yJUnJnL.png", "/srv/numbas/media/question-resources/hw1sol5_yJUnJnL.png"], ["question-resources/setDomain.html", "/srv/numbas/media/question-resources/setDomain.html"], ["question-resources/angle2_BJfRm8m.png", "/srv/numbas/media/question-resources/angle2_BJfRm8m.png"], ["question-resources/hw1sol5_oDaO6gW.png", "/srv/numbas/media/question-resources/hw1sol5_oDaO6gW.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Vectors 5 with solution", "tags": [], "metadata": {"description": "<p>Resultant force</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>Two forces $P_1=\\var{P1}\\;\\text{kN}$ and $P_2=\\var{P2}\\;\\text{kN}$&nbsp;are applied at Point <i>B</i> of beam <i>AB</i>.&nbsp;</p>\n<p><img src=\"resources/question-resources/Fig1-5_PhexlpW.png\" width=\"324\" height=\"159\"/></p>", "advice": "<p><img src=\"resources/question-resources/hw1sol5_oDaO6gW.png\"/></p>\n<p>(a) Using the law of cosines:</p>\n<p style=\"text-align: center;\">$R^2=(\\var{P1}\\;\\text{kN})^2+(\\var{P2}\\; \\text{kN})^2-2(\\var{P1}\\;\\text{kN})(\\var{P2}\\;\\text{kN})\\cos 80^\\circ$</p>\n<p style=\"text-align: right;\">$R=\\var{R}\\;\\text{kN}$&nbsp; \u25c0</p>\n<p style=\"text-align: left;\">(b) Using the law of sines</p>\n<p style=\"text-align: center;\">$\\dfrac{\\sin \\gamma}{\\var{P1}\\;\\text{kN}}=\\dfrac{\\sin 80^\\circ}{R}$</p>\n<p style=\"text-align: center;\">$\\gamma=\\var{gamma}^\\circ$</p>\n<p style=\"text-align: left; padding-left: 30px;\">In the triangle</p>\n<p style=\"padding-left: 30px; text-align: center;\">$\\beta+\\gamma+80^\\circ=180^\\circ$</p>\n<p style=\"padding-left: 30px; text-align: center;\">$\\beta=\\var{beta}^\\circ$</p>\n<p style=\"padding-left: 30px; text-align: center;\">$\\phi=180^\\circ-\\beta-50^\\circ=\\var{phi}^\\circ$</p>\n<p style=\"padding-left: 30px; text-align: right;\">$\\phi=\\var{phi}^\\circ$ \u29aa&nbsp;\u25c0</p>\n<p style=\"text-align: center;\"></p>", "rulesets": {}, "extensions": [], "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "60", "description": "", "templateType": "number"}, "gamma": {"name": "gamma", "group": "Ungrouped variables", "definition": "precround(degrees(arcsin({P1}/{R}*sin(radians(80)))),2)", "description": "", "templateType": "anything"}, "phi": {"name": "phi", "group": "Ungrouped variables", "definition": "180-50-beta", "description": "<p>;;precround(90+a-degrees(arcsin({P2}/{R}*sin(radians(180-a-b)))),2)</p>", "templateType": "anything"}, "P1": {"name": "P1", "group": "Ungrouped variables", "definition": "random(2 .. 8#1)", "description": "", "templateType": "randrange"}, "beta": {"name": "beta", "group": "Ungrouped variables", "definition": "180-gamma-80", "description": "", "templateType": "anything"}, "R": {"name": "R", "group": "Ungrouped variables", "definition": "precround(sqrt({P1}^2+{P2}^2-2*{P1}*{P2}*cos(radians(180-{a}-{b}))),2)", "description": "", "templateType": "anything"}, "P2": {"name": "P2", "group": "Ungrouped variables", "definition": "{P1}+3", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "40", "description": "", "templateType": "number"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["P1", "P2", "R", "a", "b", "phi", "gamma", "beta"], "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 their resultant (in kN) using the triangle rule.</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"}, {"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 direction of the resultant. (in degrees, measured from the horizontal axis&nbsp;<img src=\"resources/question-resources/angle2_BJfRm8m.png\" width=\"25\" height=\"16\"/>&nbsp;)</p>", "minValue": "{phi}-0.5", "maxValue": "{phi}+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/"}]}