// Numbas version: finer_feedback_settings {"name": "Vectors - Ex. Sheet 3", "percentPass": "0", "navigation": {"showfrontpage": false, "onleave": {"action": "none", "message": ""}, "showresultspage": "oncompletion", "preventleave": true, "browse": true, "allowregen": true, "reverse": true}, "timing": {"allowPause": true, "timedwarning": {"action": "none", "message": ""}, "timeout": {"action": "none", "message": ""}}, "duration": 0, "feedback": {"showtotalmark": true, "allowrevealanswer": true, "advicethreshold": 0, "showanswerstate": true, "showactualmark": true, "intro": "", "feedbackmessages": [], "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "never"}, "showstudentname": true, "question_groups": [{"name": "Group", "pickQuestions": 1, "pickingStrategy": "all-ordered", "questions": [{"name": "resultant displacement", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}], "tags": ["rebel", "REBEL", "Rebel", "rebelmaths", "resultant displacement"], "metadata": {"description": "

resultant displacement

rebelmaths

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{name1} travels {a} km east and then {b} km south. Determine how far {name1} is from his starting point and give his bearings with respect to the eastward direction.

Distance [[0]] km (to the nearest km)

Angle: East [[1]] $^\\circ$ South (to the nearest degree)

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Some the following were too skinny and so were removed.

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use https://www.mathsisfun.com/numbers/pythagorean-triples.html

so always integer and we could scale by k for more randomness.

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top of triangle for jsxgraph, keeping same ratios.

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\n//tRot.bindTo(vtext);\n\n\n\n\nreturn div;\n\n"}, "triangle": {"parameters": [], "type": "html", "language": "javascript", "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',{boundingBox:[-13,13,17,-17],grid:false,axis:false});\nvar board = div.board;\n\n//Doesn't look like you need this\nJXG.Options.text.useMathJax = true;\n\n// get the height of the triangle\nTT = Numbas.jme.unwrapValue(scope.variables.tritop);\ndx = Numbas.jme.unwrapValue(scope.variables.deltax);\nh = Numbas.jme.unwrapValue(scope.variables.h);\nv = Numbas.jme.unwrapValue(scope.variables.v);\nd = Numbas.jme.unwrapValue(scope.variables.d);\n\n\n// create the horizontal line\nvar hor = board.create('line',[[-12,-TT],[12,-TT]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the vertical line\nvar vert = board.create('line',[[12,-TT],[12,TT]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the diagonal line\nvar vert = board.create('line',[[-12,-TT],[12,TT]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//create the box for right angle\nboard.create('line',[[(12-0.1*TT),-TT],[(12-0.1*TT),-TT*0.9]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\nboard.create('line',[[(12-0.1*TT),-TT*0.9],[12,-TT*0.9]], { straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true});\n\n//label the angle theta\nboard.create('text',[-7.2,-4*TT/5,\n function() { \n return '$\\\\theta$';\n }], {fontSize:20,fixed: true});\n\n//label the angle phi\nboard.create('text',[9.6,3*TT/5,\n function() { \n return '$\\\\phi$';\n }], {fontSize:20,fixed: true});\n\n//display the side lengths\nvar vtext= board.create('text',[12.5,0,v], {fontSize:20,fixed: true});\nvar htext= board.create('text',[0,-TT-1,h], {fontSize:20,fixed: true});\nvar dtext= board.create('text',[0,TT/2+0.3,d], {fontSize:20,fixed: true});\n\n//can't figure out how to rotate text. http://jsxgraph.uni-bayreuth.de/wiki/index.php/Texts_and_Transformations suggests the following\n//var tRot = board.create('transform', [Math.PI/2, 13,0], {type:'rotate'}); 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{name[0]} wants to fire a rocket so that its {component[0][0]} velocity is {component[0][1]} $\\mathrm{ms^{-1}}$ and its {component[1][0]} velocity is {component[1][1]} $\\mathrm{ms^{-1}}$. At what angle from the horizontal should {name[1]} aim the rocket?

[[0]] $^\\circ$ (to the nearest degree).

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You have not given your answer to the correct precision.

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", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "if(vec1[2]=1,triples[2],'')", "description": "

use https://www.mathsisfun.com/numbers/pythagorean-triples.html

so always integer and we could scale by k for more randomness.

top of triangle for jsxgraph, keeping same ratios.

[[0]] $^\\circ$ (to the nearest degree).

You have not given your answer to the correct precision.

Find the work done by a force $\\mathbf{F}=$ {f1}$\\mathbf{i}+$ {f2}$\\mathbf{j}+${f3}$\\mathbf{k}$ in moving an object from the point P({p1},{p2},{p3}) to the point Q({q1},{q2},{q3}).

[[0]] Joules

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First find the displacement vector $\\simplify{vec:d}$= $\\simplify{vec:PQ}$.

Note

$\\simplify{vec:d =vec:PQ =vec:Q-vec:P}$.

Work done$=$ $\\simplify{vec:F}$ $\\cdot$ $\\simplify{vec:d}$ (Scalar Product)

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rebelmaths

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Practical questions

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