// Numbas version: exam_results_page_options
{"name": "Vector addition by summing scalar components", "extensions": ["geogebra", "weh", "quantities"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"D": {"definition": "vector(0,-8)", "name": "D", "description": "", "templateType": "anything", "group": "Inputs"}, "units": {"definition": "random(['ft','lb'],['in','lb'],['cm','N'])", "name": "units", "description": "", "templateType": "anything", "group": "Inputs"}, "A1": {"definition": "vector(-5,0)", "name": "A1", "description": "<p>Position of point A</p>", "templateType": "anything", "group": "Inputs"}, "debug": {"definition": "false", "name": "debug", "description": "", "templateType": "anything", "group": "Inputs"}, "C1": {"definition": "vector(5,0)\n", "name": "C1", "description": "<p>Position of point C</p>", "templateType": "anything", "group": "Inputs"}, "resultant": {"definition": "qty(abs(FR),units[1]) scale", "name": "resultant", "description": "", "templateType": "anything", "group": "Outputs"}, "ref": {"definition": "0", "name": "ref", "description": "<p>placeholder for reference axis</p>", "templateType": "anything", "group": "Outputs"}, "FB": {"definition": "vector(random(-5..5),random(-5..5 except 0))", "name": "FB", "description": "", "templateType": "anything", "group": "Inputs"}, "FA": {"definition": "vector(random(-5..5 except 0),random(-5..5))", "name": "FA", "description": "", "templateType": "anything", "group": "Inputs"}, "theta": {"definition": "degrees(atan2(FR[1],FR[0]))", "name": "theta", "description": "", "templateType": "anything", "group": "Outputs"}, "FC": {"definition": "vector(random(-5..5 except 0),random(-5..5 except 0))", "name": "FC", "description": "", "templateType": "anything", "group": "Inputs"}, "B1": {"definition": "vector(0,0)\n", "name": "B1", "description": "<p>Position of point B</p>", "templateType": "anything", "group": "Inputs"}, "FR": {"definition": "FA + FB + FC", "name": "FR", "description": "", "templateType": "anything", "group": "Outputs"}, "scale": {"definition": "random(0.1,0.2,0.5,2,4,5,10,20)", "name": "scale", "description": "", "templateType": "anything", "group": "Inputs"}, "angle_from_ref": {"definition": "let(ang,theta,\n[if(ang>180,ang-360,ang),\nif(ang>270,ang-450,if(ang < -90,ang+270,ang-90)),\nif(ang>0,ang-180,ang+180),\nif(ang>90,ang-270,90+ang)])", "name": "angle_from_ref", "description": "", "templateType": "anything", "group": "Outputs"}}, "advice": "<p>Vector Addition: &nbsp;</p>\n<p>$R_x = \\Sigma F_x = \\var{scale FA[0]}+\\var{scale FB[0]}+\\var{scale FC[0]} =\\var{scale FR[0]}$ {units[1]}</p>\n<p>$R_y = \\Sigma F_y = \\var{scale FA[1]}+\\var{scale FB[1]}+\\var{scale FC[1]} =\\var{scale FR[1]}$&nbsp;{units[1]}</p>\n<p>$R=\\sqrt{R_x^2 + R_y^2}&nbsp;= \\var{siground(resultant,4)}$&nbsp;</p>\n<p>$\\theta = \\tan^{-1}\\left(\\left|\\frac{R_y}{R_x}\\right| \\right) =$ {siground(degrees(arctan(FR[0]/FR[1])),4)}&deg;</p>\n<p></p>", "metadata": {"description": "<p>Add three vectors by determining their scalar components and summing them.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "functions": {}, "variablesTest": {"condition": "abs(FR) >=3", "maxRuns": "100"}, "statement": "<p><strong></strong>Three forces, <strong style=\"color: red;\">A</strong>, <strong style=\"color: blue;\">B</strong>, and <strong style=\"color: green;\">C</strong>&nbsp;are drawn&nbsp;to scale of 1 square = 1 unit squared. &nbsp;Find the resultant by summing scalar components.</p>\n<p>{geogebra_applet('vpfnqe8q', [['fa',FA],['fb',FB],['fc',FC]])}</p>\n<p></p>", "ungrouped_variables": [], "name": "Vector addition by summing scalar components", "rulesets": {}, "variable_groups": [{"name": "Inputs", "variables": ["A1", "FA", "B1", "FB", "C1", "FC", "units", "debug", "D", "scale"]}, {"name": "Outputs", "variables": ["FR", "theta", "ref", "angle_from_ref", "resultant"]}], "parts": [{"variableReplacements": [], "unitTests": [], "extendBaseMarkingAlgorithm": true, "sortAnswers": false, "type": "gapfill", "prompt": "<p>First, find the scalar components of the&nbsp;three vectors.&nbsp;</p>\n<p>$A_x =$&nbsp;[[0]]&nbsp; $B_x =$&nbsp;[[2]]&nbsp; $C_x =$&nbsp;[[4]]</p>\n<p>$A_y =$&nbsp;[[1]]&nbsp; $B_y =$&nbsp;[[3]]&nbsp; $C_y =$&nbsp;[[5]]</p>", "gaps": [{"variableReplacements": [], "unitTests": [], "extendBaseMarkingAlgorithm": true, "minValue": "{FA[0]}", "type": "numberentry", "mustBeReduced": false, "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "correctAnswerStyle": "plain", "scripts": {}, "marks": 1, "showCorrectAnswer": true, "maxValue": "{FA[0]}", "showFeedbackIcon": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": ""}, {"variableReplacements": [], "unitTests": [], "extendBaseMarkingAlgorithm": true, "minValue": "{FA[1]}", "type": "numberentry", "mustBeReduced": false, "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "correctAnswerStyle": "plain", "scripts": {}, "marks": 1, "showCorrectAnswer": true, "maxValue": "{FA[1]}", "showFeedbackIcon": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": ""}, {"variableReplacements": [], "unitTests": [], "extendBaseMarkingAlgorithm": true, "minValue": "{FB[0]}", "type": "numberentry", "mustBeReduced": false, "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "correctAnswerStyle": "plain", "scripts": {}, "marks": 1, "showCorrectAnswer": true, "maxValue": "{FB[0]}", "showFeedbackIcon": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": ""}, {"variableReplacements": [], "unitTests": [], "extendBaseMarkingAlgorithm": true, "minValue": "{FB[1]}", "type": "numberentry", "mustBeReduced": false, "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "correctAnswerStyle": "plain", "scripts": {}, "marks": 1, "showCorrectAnswer": true, "maxValue": "{FB[1]}", "showFeedbackIcon": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": ""}, {"variableReplacements": [], "unitTests": [], "extendBaseMarkingAlgorithm": true, "minValue": "{FC[0]}", "type": "numberentry", "mustBeReduced": false, "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "correctAnswerStyle": "plain", "scripts": {}, "marks": 1, "showCorrectAnswer": true, "maxValue": "{FC[0]}", "showFeedbackIcon": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": ""}, {"variableReplacements": [], "unitTests": [], "extendBaseMarkingAlgorithm": true, "minValue": "{FC[1]}", "type": "numberentry", "mustBeReduced": false, "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "correctAnswerStyle": "plain", "scripts": {}, "marks": 1, "showCorrectAnswer": true, "maxValue": "{FC[1]}", "showFeedbackIcon": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": ""}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "customMarkingAlgorithm": ""}, {"variableReplacements": [], "unitTests": [], "extendBaseMarkingAlgorithm": true, "sortAnswers": false, "type": "gapfill", "prompt": "<p>Find the sum of the three vectors&nbsp;<strong>R</strong>, by adding the scalar components.</p>\n<p>$R_x&nbsp; = A_x + B_x + C_x =$&nbsp;[[0]]&nbsp;</p>\n<p>$R_y&nbsp; = A_y + B_y + C_y =$ [[1]]&nbsp;&nbsp;</p>", "gaps": [{"variableReplacements": [], "unitTests": [], "extendBaseMarkingAlgorithm": true, "minValue": "{FA[0]}+{FB[0]}+{FC[0]}", "type": "numberentry", "mustBeReduced": false, "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "correctAnswerStyle": "plain", "scripts": {}, "marks": 1, "showCorrectAnswer": true, "maxValue": "{FA[0]}+{FB[0]}+{FC[0]}", "showFeedbackIcon": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": ""}, {"variableReplacements": [], "unitTests": [], "extendBaseMarkingAlgorithm": true, "minValue": "{FA[1]}+{FB[1]}+{FC[1]}", "type": "numberentry", "mustBeReduced": false, "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "correctAnswerStyle": "plain", "scripts": {}, "marks": 1, "showCorrectAnswer": true, "maxValue": "{FA[1]}+{FB[1]}+{FC[1]}", "showFeedbackIcon": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": ""}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "customMarkingAlgorithm": ""}], "preamble": {"css": "", "js": ""}, "tags": [], "extensions": ["geogebra", "quantities", "weh"], "type": "question", "contributors": [{"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}