// Numbas version: finer_feedback_settings
{"name": "Find magnitude and direction of three vectors", "extensions": ["geogebra", "weh", "quantities"], "custom_part_types": [{"source": {"pk": 24, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/24/edit"}, "name": "Angle quantity", "short_name": "angle-quantity-from-reference", "description": "<p>Angle&nbsp;as a quantity in degrees.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['correct_quantity'])", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\ncorrect_scalar:\nscalar(correct_quantity)\n  \n\ncorrect_quantity:\nsettings['correct_quantity']\n\ncorrect_units:\nunits(correct_quantity)\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\njoin(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n\n\ngood_units:\ntry(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)\n\nstudent_quantity:\nswitch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)\n\nangle_in_range:\nif(settings['restrict_angle'], abs(student_scalar) <= 90, true)\n\nright:\nwithinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])\n\nclose:\nwithinTolerance(student_scalar, correct_scalar, settings['close'])", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \nright and good_units and right_sign and angle_in_range, add_credit(1.0,'Correct.'),\nright and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\nright and right_sign and not good_units, add_credit(settings['C2'],'Correct angle, but missing degree symbol.'),\nright and good_units and right_sign and not angle_in_range,add_credit(settings['C1'],'Angle is out of range.'),\nclose and good_units, add_credit(settings['C1'],'Close.'),\nclose and not good_units, add_credit(settings['C3'],'Answer is close, but missing degree symbol.'),\nincorrect('Wrong answer.')\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)"}, {"name": "correct_scalar", "description": "", "definition": "scalar(correct_quantity)\n  "}, {"name": "correct_quantity", "description": "", "definition": "settings['correct_quantity']"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "", "definition": "join(\nsplit(studentAnswer[len(match_student_number[0])..len(studentAnswer)]\n,\"\u00b0\"),\" deg\")\n\n"}, {"name": "good_units", "description": "", "definition": "try(\nkind(quantity(1, student_units))= kind(correct_quantity),\nmsg,\nfeedback(msg);false)"}, {"name": "student_quantity", "description": "", "definition": "switch(not good_units, \nstudent_scalar * correct_units, \nnot right_sign,\n-quantity(student_scalar, student_units),\nquantity(student_scalar,student_units)\n)"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity)"}, {"name": "angle_in_range", "description": "", "definition": "if(settings['restrict_angle'], abs(student_scalar) <= 90, true)"}, {"name": "right", "description": "<p>Will check for correct sign elswhere.</p>", "definition": "withinTolerance(abs(student_scalar), abs(correct_scalar), settings['right'])"}, {"name": "close", "description": "<p>Must have correct sign to be close.</p>", "definition": "withinTolerance(student_scalar, correct_scalar, settings['close'])\n"}], "settings": [{"name": "correct_quantity", "label": "Correct Angle as quantity ", "help_url": "", "hint": "", "input_type": "code", "default_value": "qty(45,'deg')", "evaluate": true}, {"name": "right", "label": "Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.1", "evaluate": true}, {"name": "restrict_angle", "label": "Less than 90\u00b0", "help_url": "", "hint": "When checked, angle must be between -90&deg; and +90&deg;.", "input_type": "checkbox", "default_value": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units.", "input_type": "percent", "default_value": "75"}, {"name": "close", "label": " Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within &plusmn; this amount from the correct value.", "input_type": "code", "default_value": "0.5", "evaluate": true}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value without units.", "input_type": "percent", "default_value": "25"}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "variable_groups": [{"variables": ["A1", "FA", "B1", "FB", "C1", "FC", "units", "debug", "scale"], "name": "Inputs"}, {"variables": ["mag_a", "theta_a", "mag_b", "theta_b", "mag_c", "theta_c"], "name": "Outputs"}], "tags": [], "name": "Find magnitude and direction of three vectors", "functions": {}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": "<p>Given three vectors with integer components, find the corresponding magnitude and direction.</p>"}, "ungrouped_variables": ["a_from_ref", "b_from_ref", "c_from_ref", "ref"], "parts": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "variableReplacements": [], "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "gaps": [{"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "unitTests": [], "settings": {"correctAnswer": "mag_A", "right": "0.2", "C2": "50", "C1": "75", "C3": "25", "close": "1.0"}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "engineering-answer", "variableReplacements": [], "scripts": {}, "marks": "4"}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "unitTests": [], "settings": {"dummy": "'ignore'"}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "drop-down-axis-reference", "variableReplacements": [], "scripts": {"mark": {"script": "index = Numbas.jme.unwrapValue(this.studentAnswerAsJME());\nangles = Numbas.jme.unwrapValue(Numbas.exam.currentQuestion.scope.getVariable('a_from_ref'));\nans = Qty(angles[index]+' deg');\nthis.parentPart.gaps[2].settings.correct_quantity.value=ans;\nthis.markingComment(\"For your axis, the direction is \" + ans.toPrec('0.1 deg').toString() +'.');", "order": "after"}}, "marks": "0"}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "unitTests": [], "settings": {"correct_quantity": "qty(a_from_ref[ref],'deg')", "C3": "25", "C2": "50", "right": "0.2", "C1": "75", "restrict_angle": true, "close": "1.0"}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "angle-quantity-from-reference", "variableReplacements": [], "scripts": {}, "marks": "4"}], "type": "gapfill", "prompt": "<p>Find the magnitude and direction of <strong style=\"color: red;\">A</strong>.</p>\n<p>$A$&nbsp;=&nbsp;[[0]]</p>\n<p>&nbsp;$\\theta_A$ =&nbsp;[[2]]&nbsp;measured from the&nbsp;&nbsp;[[1]]</p>\n<p><span data-jme-visible=\"debug\">magnitude&nbsp;= {siground(mag_A,4)} </span></p>\n<p><span data-jme-visible=\"debug\">direction={theta_A} &nbsp;{a_from_ref}</span></p>"}, {"variableReplacementStrategy": "originalfirst", "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "variableReplacements": [], "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "gaps": [{"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "unitTests": [], "settings": {"correctAnswer": "mag_B", "right": "0.2", "C2": "50", "C1": "75", "C3": "25", "close": "1.0"}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "engineering-answer", "variableReplacements": [], "scripts": {}, "marks": "4"}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "unitTests": [], "settings": {"dummy": "'ignore'"}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "drop-down-axis-reference", "variableReplacements": [], "scripts": {"mark": {"script": "index = Numbas.jme.unwrapValue(this.studentAnswerAsJME());\nangles = Numbas.jme.unwrapValue(Numbas.exam.currentQuestion.scope.getVariable('b_from_ref'));\nans = Qty(angles[index]+' deg');\nthis.parentPart.gaps[2].settings.correct_quantity.value=ans;\nthis.markingComment(\"For your axis, the direction is \" + ans.toPrec('0.1 deg').toString() +'.');", "order": "after"}}, "marks": "0"}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "unitTests": [], "settings": {"correct_quantity": "qty(b_from_ref[ref],'deg')", "C3": "25", "C2": "50", "right": "0.2", "C1": "75", "restrict_angle": true, "close": "1.0"}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "angle-quantity-from-reference", "variableReplacements": [], "scripts": {}, "marks": "4"}], "type": "gapfill", "prompt": "<p>Find the magnitude and direction of <strong style=\"color: blue;\">B</strong>.</p>\n<p>$B$&nbsp;=&nbsp;[[0]]</p>\n<p>&nbsp;$\\theta_B$ =&nbsp;[[2]]&nbsp;measured from the&nbsp;&nbsp;[[1]]</p>\n<p><span data-jme-visible=\"debug\">magnitude&nbsp;= {siground(mag_B,4)} </span></p>\n<p><span data-jme-visible=\"debug\">direction={theta_B} {b_from_ref}&nbsp;</span></p>"}, {"variableReplacementStrategy": "originalfirst", "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "variableReplacements": [], "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "gaps": [{"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "unitTests": [], "settings": {"correctAnswer": "mag_B", "right": "0.2", "C2": "50", "C1": "75", "C3": "25", "close": "1.0"}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "engineering-answer", "variableReplacements": [], "scripts": {}, "marks": "4"}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "unitTests": [], "settings": {"dummy": "'ignore'"}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "drop-down-axis-reference", "variableReplacements": [], "scripts": {"mark": {"script": "index = Numbas.jme.unwrapValue(this.studentAnswerAsJME());\nangles = Numbas.jme.unwrapValue(Numbas.exam.currentQuestion.scope.getVariable('c_from_ref'));\nans = Qty(angles[index]+' deg');\nthis.parentPart.gaps[2].settings.correct_quantity.value=ans;\nthis.markingComment(\"For your axis, the direction is \" + ans.toPrec('0.1 deg').toString() +'.');", "order": "after"}}, "marks": "0"}, {"variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "unitTests": [], "settings": {"correct_quantity": "qty(b_from_ref[ref],'deg')", "C3": "25", "C2": "50", "right": "0.2", "C1": "75", "restrict_angle": true, "close": "1.0"}, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "angle-quantity-from-reference", "variableReplacements": [], "scripts": {}, "marks": "4"}], "type": "gapfill", "prompt": "<p>Find the magnitude and direction of <strong style=\"color: green;\">C</strong>.</p>\n<p>$C$&nbsp;=&nbsp;[[0]]</p>\n<p>&nbsp;$\\theta_C$ =&nbsp;[[2]]&nbsp;measured from the&nbsp;&nbsp;[[1]]</p>\n<p><span data-jme-visible=\"debug\">magnitude&nbsp;= {siground(mag_C,4)} </span></p>\n<p><span data-jme-visible=\"debug\">direction={theta_C} {C_from_ref}&nbsp;</span></p>"}], "variablesTest": {"maxRuns": "100", "condition": "abs(FA)>=3 and abs(FB)>=3 and abs(FC)>=3"}, "variables": {"ref": {"description": "<p>placeholder for reference axis</p>", "definition": "0", "templateType": "anything", "name": "ref", "group": "Ungrouped variables"}, "mag_c": {"description": "", "definition": "qty(abs(FC),units[1]) scale", "templateType": "anything", "name": "mag_c", "group": "Outputs"}, "FC": {"description": "", "definition": "vector(random(-5..5 except 0),random(-5..5 except 0))", "templateType": "anything", "name": "FC", "group": "Inputs"}, "a_from_ref": {"description": "", "definition": "let(ang,theta_a,\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)])", "templateType": "anything", "name": "a_from_ref", "group": "Ungrouped variables"}, "A1": {"description": "<p>Position of point A &nbsp;(start point for force A) &nbsp;fixed in this problem</p>", "definition": "vector(-5,0)", "templateType": "anything", "name": "A1", "group": "Inputs"}, "B1": {"description": "<p>Position of point B</p>", "definition": "vector(0,0)\n", "templateType": "anything", "name": "B1", "group": "Inputs"}, "c_from_ref": {"description": "", "definition": "let(ang,theta_c,\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)])\n", "templateType": "anything", "name": "c_from_ref", "group": "Ungrouped variables"}, "C1": {"description": "<p>Position of point C</p>", "definition": "vector(5,0)\n", "templateType": "anything", "name": "C1", "group": "Inputs"}, "theta_b": {"description": "", "definition": "degrees(atan2(FB[1],FB[0]))", "templateType": "anything", "name": "theta_b", "group": "Outputs"}, "scale": {"description": "", "definition": "random(0.1,0.25,0.5,2,4,5,10,20)", "templateType": "anything", "name": "scale", "group": "Inputs"}, "FB": {"description": "", "definition": "vector(random(-5..5),random(-5..5 except 0))", "templateType": "anything", "name": "FB", "group": "Inputs"}, "theta_c": {"description": "", "definition": "degrees(atan2(FC[1],FC[0]))", "templateType": "anything", "name": "theta_c", "group": "Outputs"}, "mag_b": {"description": "", "definition": "qty(abs(FB),units[1]) scale", "templateType": "anything", "name": "mag_b", "group": "Outputs"}, "mag_a": {"description": "", "definition": "qty(abs(FA),units[1]) scale", "templateType": "anything", "name": "mag_a", "group": "Outputs"}, "FA": {"description": "", "definition": "vector(random(-5..5 except 0),random(-5..5))", "templateType": "anything", "name": "FA", "group": "Inputs"}, "units": {"description": "", "definition": "random(['ft','lb'],['in','lb'],['cm','N'])", "templateType": "anything", "name": "units", "group": "Inputs"}, "b_from_ref": {"description": "", "definition": "let(ang,theta_b,\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)])\n", "templateType": "anything", "name": "b_from_ref", "group": "Ungrouped variables"}, "theta_a": {"description": "", "definition": "degrees(atan2(FA[1],FA[0]))", "templateType": "anything", "name": "theta_a", "group": "Outputs"}, "debug": {"description": "", "definition": "false", "templateType": "anything", "name": "debug", "group": "Inputs"}}, "extensions": ["geogebra", "quantities", "weh"], "type": "question", "preamble": {"js": "", "css": ""}, "advice": "<p>For force $\\textbf{A}$</p>\n<p>$A = \\sqrt{{A_x}^2 + {A_y}^2} = \\sqrt{\\var{FA[0]}^2 +\\var{FA[1]}^2}$ = {siground(mag_A,4)}</p>\n<p>$\\theta_A = \\tan^{-1}\\left(\\left|\\dfrac{A_y}{A_x}\\right|\\right) =&nbsp;\\tan^{-1}\\left(\\left|\\dfrac{\\var{FA[1]}}{\\var{FA[0]}}\\right|\\right) =\\var{siground(degrees(arctan(abs(FA[1]/FA[0]))),4)}&deg;$</p>\n<p>and similarly for $\\textbf{B}$ and $\\textbf{C}$.</p>", "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 = {scale} {units[1]}. &nbsp;Find the magnitude and direction of each.</p>\n<p>{geogebra_applet('qdbwtfa9', [['fa',FA],['fb',FB],['fc',FC]])}</p>\n<p></p>", "contributors": [{"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}