A few questions which use the GeoGebra extension.
", "licence": "Creative Commons Attribution 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": true, "showstudentname": true, "question_groups": [{"name": "Loading GeoGebra worksheets", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "questions": [{"name": "Create a GeoGebra worksheet entirely in Numbas", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "This question shows how to use the GeoGebra extension to start with a blank worksheet, and add objects to it.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "The diagram below shows points at $\\var{p1}$ and $\\var{p2}$, as well as their midpoint.
\n{app}
", "advice": "", "rulesets": {}, "variables": {"app": {"name": "app", "group": "Ungrouped variables", "definition": "geogebra_applet(\n 800,500,\n [\n A: [\n definition: p1,\n label_visible: false\n ],\n B: [\n definition: p2,\n label_visible: false\n ],\n m: [\n definition: \"Midpoint(A,B)\",\n label_visible: false\n ]\n ]\n)", "description": "", "templateType": "anything"}, "p1": {"name": "p1", "group": "Ungrouped variables", "definition": "vector(random(-5..-2), random(-4..4 except 0))", "description": "", "templateType": "anything"}, "p2": {"name": "p2", "group": "Ungrouped variables", "definition": "vector(random(2..5), random(-4..4 except 0))", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["p1", "p2", "app"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Load a GeoGebra worksheet from a file", "extensions": ["geogebra"], "custom_part_types": [], "resources": [["question-resources/material-dw4n67kf_vCI9659.ggb", "/srv/numbas/media/question-resources/material-dw4n67kf_vCI9659.ggb"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "This question demonstrates how to display a GeoGebra worksheet loaded from a file attached to the question.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "The diagram below has been loaded from a file.
\nThe point $A$ has been moved to $\\var{A}$ and locked.
\n{geogebra_file('material-dw4n67kf_vCI9659.ggb',[\"A\":[\"definition\": A, \"fixed\": true]])}
", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "vector(random(0..2),random(0..2))", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Load a GeoGebra worksheet from geogebra.org", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "This question shows how to load a GeoGebra applet from geogebra.org.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "This worksheet has been loaded from https://www.geogebra.org/m/UqJChZFJ
\n{geogebra_applet('https://www.geogebra.org/m/UqJChZFJ')}
", "advice": "", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Marking", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "questions": [{"name": "Mark a part as correct if the student moves a point to the right position", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "The student is shown a GeoGebra worksheet containing a single point on a grid. They must move the point to the required coordinates.
\nThe part is marked as correct if the point is in the right position.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"app": {"name": "app", "group": "Ungrouped variables", "definition": "geogebra_applet(\n 800,500,\n [\n \"A\": [\n \"definition\": vector(0,0),\n \"label_visible\": false\n ]\n ],\n [\n [\"A\", \"p0\"]\n ]\n)", "description": "", "templateType": "anything"}, "target_position": {"name": "target_position", "group": "Ungrouped variables", "definition": "vector(\n random(-2..2 except 0),\n random(-2..2 except 0)\n)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["app", "target_position"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "extension", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "pos:\n value(app,\"A\")\n\nmark:\n feedback(\"The point is at $\"+latex(app,'A')+\"$.\");\n correctif(pos=target_position)\n\ninterpreted_answer:\n pos", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "{app}
\nMove the point to $\\var[rowvector]{target_position}$.
"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Construct a polygon point by point", "extensions": ["geogebra"], "custom_part_types": [{"source": {"pk": 1, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/1/edit"}, "name": "Yes/no", "short_name": "yes-no", "description": "The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.
", "help_url": "", "input_widget": "radios", "input_options": {"correctAnswer": "if(eval(settings[\"correct_answer_expr\"]), 0, 1)", "hint": {"static": true, "value": ""}, "choices": {"static": true, "value": ["Yes", "No"]}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nif(studentanswer=correct_answer,\n correct(),\n incorrect()\n)\n\ninterpreted_answer:\nstudentAnswer=0\n\ncorrect_answer:\nif(eval(settings[\"correct_answer_expr\"]),0,1)", "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": "if(studentanswer=correct_answer,\n correct(),\n incorrect()\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer=0"}, {"name": "correct_answer", "description": "", "definition": "if(eval(settings[\"correct_answer_expr\"]),0,1)"}], "settings": [{"name": "correct_answer_expr", "label": "Is the answer \"Yes\"?", "help_url": "", "hint": "An expression which evaluates totrue or false.", "input_type": "mathematical_expression", "default_value": "true", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "This question demonstrates how to use GeoGebra applets in explore mode.
\nThe student must construct a polygon by adding points one at a time. At any point, they can answer the question, \"Is the centroid inside the polygon?\"
\nGeoGebra's IsInRegion command is used to decide if the centroid is inside the polygon.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"points": {"name": "points", "group": "Ungrouped variables", "definition": "[\n vector(0,0),\n vector(1,0)\n]", "description": "", "templateType": "anything", "can_override": false}, "centroid": {"name": "centroid", "group": "Ungrouped variables", "definition": "vector(\n sum_x,\n sum_y\n)/len(points)", "description": "", "templateType": "anything", "can_override": false}, "sum_x": {"name": "sum_x", "group": "Ungrouped variables", "definition": "sum(map(v[0],v,points))", "description": "", "templateType": "anything", "can_override": false}, "sum_y": {"name": "sum_y", "group": "Ungrouped variables", "definition": "sum(map(v[1],v,points))", "description": "", "templateType": "anything", "can_override": false}, "show_centroid_applet": {"name": "show_centroid_applet", "group": "Ungrouped variables", "definition": "geogebra_applet(500,500,\n [\n \"points\": [\n \"definition\": points,\n \"visible\": true\n ],\n \"p\": \"Polygon(points)\",\n \"C\": [\n \"definition\": centroid,\n \"fixed\": true\n ],\n \"contained\": \"IsInRegion(C,p)\"\n ]\n)", "description": "An applet showing the position of the centroid.
", "templateType": "anything", "can_override": false}, "show_points_applet": {"name": "show_points_applet", "group": "Ungrouped variables", "definition": "geogebra_applet(500,500,\n [\n \"points\": [\n \"definition\": points,\n \"visible\": true\n ],\n \"p\": \"Polygon(points)\"\n ]\n)", "description": "An applet showing just the points defined so far.
", "templateType": "anything", "can_override": false}, "test_centroid_applet": {"name": "test_centroid_applet", "group": "Ungrouped variables", "definition": "geogebra_applet(500,500,\n [\n \"points\": points,\n \"p\": \"Polygon(points)\",\n \"C\": [\n \"definition\": centroid,\n \"visible\": false\n ],\n \"contained\": \"IsInRegion(C,p)\"\n ]\n)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["points", "sum_x", "sum_y", "show_points_applet", "centroid", "show_centroid_applet", "test_centroid_applet"], "variable_groups": [], "functions": {"add_point_applet": {"parameters": [["points", "list"], ["part_path", "string"]], "type": "ggbapplet", "language": "jme", "definition": "geogebra_applet(500,500,\n [\n \"points\": [\n \"definition\": points,\n \"visible\": true\n ],\n \"p\": \"Polygon(points)\",\n \"A\": vector(0.5,0.5)\n ],\n [\n [\"A\",part_path]\n ]\n)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "matrix", "useCustomName": true, "customName": "Add a point", "marks": "0", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Show the points", "rawLabel": "", "otherPart": 1, "variableReplacements": [{"variable": "points", "definition": "points+[transpose(interpreted_answer)[0]]"}], "availabilityCondition": "answered", "penalty": "", "penaltyAmount": 0, "showPenaltyHint": true, "lockAfterLeaving": false}, {"label": "Add another point", "rawLabel": "Add another point", "otherPart": 0, "variableReplacements": [{"variable": "points", "definition": "points+[transpose(interpreted_answer)[0]]"}], "availabilityCondition": "answered", "penalty": "", "penaltyAmount": 0, "showPenaltyHint": true, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "{add_point_applet(points,part_path)}
\nAdd a point to the polygon.
\nEither write the coordinates below or move the point $A$ in the diagram above.
", "correctAnswer": "vector(0,0)", "correctAnswerFractions": false, "numRows": "2", "numColumns": 1, "allowResize": false, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "prefilledCells": ""}, {"type": "information", "useCustomName": true, "customName": "Show the points", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Is the centroid in the polygon?", "rawLabel": "", "otherPart": 2, "variableReplacements": [], "availabilityCondition": "len(points)>=3", "penalty": "", "penaltyAmount": 0, "showPenaltyHint": true, "lockAfterLeaving": false}, {"label": "Add a point", "rawLabel": "", "otherPart": 0, "variableReplacements": [], "availabilityCondition": "", "penalty": "", "penaltyAmount": 0, "showPenaltyHint": true, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "{show_points_applet}
"}, {"type": "yes-no", "useCustomName": true, "customName": "Is the centroid in the polygon?", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "correct_answer:\n if(value(test_centroid_applet,\"contained\"),0,1)", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Show the centroid", "rawLabel": "", "otherPart": 3, "variableReplacements": [], "availabilityCondition": "not (answered and credit=1)", "penalty": "", "penaltyAmount": 0, "showPenaltyHint": true, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Is the centroid in the polygon?", "prompt": "{test_centroid_applet}
\nIs the centroid of this polygon inside the polygon?
", "settings": {"correct_answer_expr": "true"}}, {"type": "information", "useCustomName": true, "customName": "Show the centroid", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "{show_centroid_applet}
\nThe centroid is at $\\var{precround(centroid,2)}$.
"}], "partsMode": "explore", "maxMarks": 0, "objectives": [{"name": "Is the centroid in the polygon?", "limit": "2"}], "penalties": [{"name": "Centroid shown", "limit": "1"}], "objectiveVisibility": "always", "penaltyVisibility": "when-active"}, {"name": "Link a GeoGebra object to a part's answer", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": [], "metadata": {"description": "This question demonstrates how to link a GeoGebra object to the answer to a part.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(-2..2 except 0)", "description": "", "templateType": "anything"}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(-2..2 except 0)", "description": "", "templateType": "anything"}, "lines_app": {"name": "lines_app", "group": "Ungrouped variables", "definition": "geogebra_applet(800,500,\n [\n \"A\": vector(0,0),\n \"l1\": [\n \"definition\": \"Line(({x},0),({x},1))\",\n \"label_visible\": false\n ],\n \"l2\": [\n \"definition\": \"Line((0,{y}),(1,{y}))\",\n \"label_visible\": false\n ]\n ],\n [\n [\"A\",\"p0\"]\n ]\n)", "description": "The applet for the first part, where the student must find the point of intersection of lines $x = \\var{x}$ and $y = \\var{y}$
", "templateType": "anything"}, "width": {"name": "width", "group": "Ungrouped variables", "definition": "random(1..height-1)", "description": "", "templateType": "anything"}, "height": {"name": "height", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "templateType": "anything"}, "area": {"name": "area", "group": "Ungrouped variables", "definition": "width*height", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "y", "lines_app", "width", "height", "area"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "matrix", "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": "{lines_app}
\nWhat is the point of intersection of the lines $x = \\var{x}$ and $y=\\var{y}$?
\nEnter the coordinates or move the point on the diagram above.
", "correctAnswer": "matrix([[x],[y]])", "correctAnswerFractions": false, "numRows": "2", "numColumns": 1, "allowResize": true, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}, {"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": "{geogebra_applet('https://www.geogebra.org/calculator/yms47z6u',[],[[\"area\",\"p1\"]])}
\nWhat is the area of a rectangle with side lengths {width} and {height}? Drag the points on the diagram above to form the rectangle, and the area will be written below.
", "minValue": "area", "maxValue": "area", "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"}]}, {"name": "Illustration", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["Motion on a slope"], "questions": [{"name": "GeoGebra test - motion on a slope", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "functions": {}, "ungrouped_variables": [], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "Either construct the intersection of two circles centred at $\\mathbf{a}$ and $\\mathbf{b}$, or use the Regular Polygon tool.
\n(I could embed another GeoGebra applet here)
", "rulesets": {}, "parts": [{"stepsPenalty": 0, "precisionType": "dp", "prompt": "What is the total force acting on the mass, along the slope? Enter your answer in $\\mathrm{N}$, to 2 decimal places.
", "precisionMessage": "You have not given your answer to the correct precision.
", "allowFractions": false, "variableReplacements": [], "maxValue": "mass*acceleration", "strictPrecision": false, "minValue": "mass*acceleration", "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "There are two forces acting on the mass: gravity and friction.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}, {"precisionType": "dp", "prompt": "What is the force due to gravity, in the direction of the slope? Enter your answer in $\\mathrm{N}$, to 2 decimal places.
", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "mass*a_gravity", "strictPrecision": false, "minValue": "mass*a_gravity", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "What is the force due to friction, in the direction of the slope? Enter your answer in $\\mathrm{N}$, to 2 decimal places.
", "precisionMessage": "You have not given your answer to the correct precision.
", "allowFractions": false, "variableReplacements": [], "maxValue": "mass*a_friction", "strictPrecision": false, "minValue": "mass*a_friction", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": "3", "type": "numberentry", "showPrecisionHint": false}, {"displayColumns": 0, "prompt": "What happens to the mass next?
", "matrix": "if(acceleration=0,[0,1,0],[1,0,0])", "shuffleChoices": false, "variableReplacements": [], "choices": ["It moves down the slope.
", "It moves up the slope.
", "It remains stationary.
"], "variableReplacementStrategy": "originalfirst", "maxMarks": 0, "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "1_n_2", "displayType": "radiogroup", "minMarks": 0}, {"precisionType": "dp", "prompt": "At what time does the mass reach the ground? Enter your answer in seconds to 2 decimal places, or $0$ if the mass never reaches the ground.
", "precisionMessage": "You have not given your answer to the correct precision.
", "allowFractions": false, "variableReplacements": [], "maxValue": "t_ground", "strictPrecision": false, "minValue": "t_ground", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "statement": "A mass of $\\var{mass}\\,\\mathrm{kg}$ is resting on a plane inclined at $\\var{incline}^{\\circ}$ to the horizontal. The distance along the plane from the ground to the mass is $\\var{distance}\\mathrm{m}$.
\nA gravitational force of $9.8\\,\\mathrm{N/kg}$ is acting on the mass, and the coefficient of friction between the plane and the mass is $\\mu = \\var{c_friction}$.
\n{geogebra_applet('xn3p5x73',[[\"height\",height],[\"c_\\{friction\\}\",c_friction],[\"mass\",mass]],[])}
", "variable_groups": [{"variables": ["height", "c_friction", "mass", "incline", "distance"], "name": "Setup"}, {"variables": ["slope", "gravity", "a_gravity", "a_friction", "acceleration_naive", "acceleration"], "name": "Acceleration"}, {"variables": ["t_ground"], "name": "Answer"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"slope": {"definition": "vector(cos(radians(incline)),sin(radians(incline)))", "templateType": "anything", "group": "Acceleration", "name": "slope", "description": ""}, "acceleration": {"definition": "if(acceleration_naive<0,acceleration_naive,0)", "templateType": "anything", "group": "Acceleration", "name": "acceleration", "description": ""}, "incline": {"definition": "precround(degrees(arctan(height/50)),1)", "templateType": "anything", "group": "Setup", "name": "incline", "description": ""}, "t_ground": {"definition": "if(acceleration=0,0,sqrt(-2*distance/acceleration))", "templateType": "anything", "group": "Answer", "name": "t_ground", "description": ""}, "distance": {"definition": "45", "templateType": "anything", "group": "Setup", "name": "distance", "description": ""}, "a_friction": {"definition": "let(f,dot(matrix([[0,1],[-1,0]])*slope,gravity)*c_friction,\n min(f,-a_gravity)\n)", "templateType": "anything", "group": "Acceleration", "name": "a_friction", "description": ""}, "c_friction": {"definition": "random(0.01..0.5#0.01)", "templateType": "anything", "group": "Setup", "name": "c_friction", "description": ""}, "gravity": {"definition": "vector(0,-9.8)", "templateType": "anything", "group": "Acceleration", "name": "gravity", "description": ""}, "a_gravity": {"definition": "dot(gravity,slope)", "templateType": "anything", "group": "Acceleration", "name": "a_gravity", "description": ""}, "mass": {"definition": "random(5..35#5)", "templateType": "anything", "group": "Setup", "name": "mass", "description": ""}, "acceleration_naive": {"definition": "a_gravity+a_friction", "templateType": "anything", "group": "Acceleration", "name": "acceleration_naive", "description": ""}, "height": {"definition": "random(10..40)", "templateType": "anything", "group": "Setup", "name": "height", "description": ""}}, "metadata": {"description": "Given the gradient of a slope and the coefficient of friction for a mass resting on it, use the equations of motion to calculate how it moves.
\nIncludes a GeoGebra rendering of the model.
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