<![CDATA[component of a Vector Model]]> false false false false false false false true true false ]]> ./horizontalvertical/2017.png ./01authorlookang50x50.png DESCRIPTION_EDITOR About true false _default_ About false

Topics

Measurement of length and time

Description

A vector is a quantity that has both magnitude and direction. Displacement, velocity, acceleration, and force are the vector quantities. in simpler examples, vectors were simply directed up, down, left or right. In situations in which vectors are directed at angles to the customary x(horizontal)-y(vertical) coordinate axes, a useful mathematical trick will be employed to transform the vector into two parts with each part being directed along the coordinate axes. For example, a vector that is directed northwest can be thought of as having two parts - a northward part and a westward part. A vector that is directed upward and rightward can be thought of as having two parts - an upward part and a rightward part.

Calculate the components of the vector A

1. click reset to generate a new random vector A of length |A| at an angle of theta to the positive x axis.
2. use the formula Ax = |A|cos(theta) to find the x direction component Ax.
3. use the formula Ay = |A|sin(theta) to find the y direction component Ay.
4. click reset to random generate a new vector A.
5. test yourself whether you have enough practice calculating Ax and Ay.

Other interesting fun activities

1. this model can be used to calculate any length |A| by keying in the values such as |A| =500 and theta = 63 degrees. Select the checkboxes Ax and Ay to see the new answers.
2. when Ax is selected, the PLAY button animates the effects of changing Ax alone.
3. when Ay is selected, the PLAY button animates the effects of changing Ay alone.
4. explore your own vector(s) here to test your understanding.
5. leave me a Google+ comment/question/requests etc here http://weelookang.blogspot.sg/2014/10/components-vector-model.html

Sample Learning Goals

(e) state what is meant by scalar and vector (how to resolve) quantities and give common examples of each
(f) calculate vector by means of components

Version:

  1. http://weelookang.blogspot.sg/2014/10/components-vector-model.html


]]> 20 5 false VARIABLE_EDITOR Var Table true false VARIABLE_EDITOR vector true false VARIABLE_EDITOR anglepolygon true false VARIABLE_EDITOR sincos true false VARIABLE_EDITOR layout true false VARIABLE_EDITOR quiz true false CODE_EDITOR axes true false CODE_EDITOR quiz true false CODE_EDITOR svg true false '+ ' '+ ' '+ ' '+ ' '+ ''; container.innerHTML = svggradient; document.body.appendChild(container); var container = document.createElement('div'); var svggradient = ''+ ' '+ ' '+ ' '+ ' '+ ''; container.innerHTML = svggradient; document.body.appendChild(container); //"url(#mygrandient1)" var container = document.createElement('div'); var svggradient = ''+ ' '+ ' '+ ' '+ ' '+ ''; container.innerHTML = svggradient; document.body.appendChild(container); //"url(#mygrandient2)" ]]> ODE_EDITOR Evol Page 2 true false EVENT_EDITOR Event true false CROSSING_EVENT BISECTION 100 true EVENT_EDITOR Event 2 true false CROSSING_EVENT BISECTION 100 true EVENT_EDITOR Event 3 true false CROSSING_EVENT BISECTION 100 true EVENT_EDITOR Event 2 2 true false CROSSING_EVENT BISECTION 100 true t dt Axcomponentmove Aycomponentmove RungeKutta 10000 0.00001 false false false false ODE_EDITOR Evol Page true false EVENT_EDITOR Event true false CROSSING_EVENT BISECTION 100 true EVENT_EDITOR Event 2 true false CROSSING_EVENT BISECTION 100 true EVENT_EDITOR Event 3 true false CROSSING_EVENT BISECTION 100 true EVENT_EDITOR Event 3 2 true false CROSSING_EVENT BISECTION 100 true EVENT_EDITOR Event 4 true false CROSSING_EVENT BISECTION 100 true EVENT_EDITOR Event 2 2 true false CROSSING_EVENT BISECTION 100 true t dt Axmovevx Aymovevy parallelv Euler 10000 0.00001 false false false false CODE_EDITOR FixRel Page true false 3.||cta<-3.){ // angledisplayx=Math.cos(cta/3); // alert(); angledisplayy=0.2; // Axtextx= Aytexty=0.5; // force |A| to above Axtexty=-0.7; // force Ax to be below if (cta>3){ ctaacute=pi-cta; ctadegreeacute=180-ctadegree; transformationangle=pi-ctaacute; } else if (cta<-3){ ctaacute=pi+cta; ctadegreeacute=+180+ctadegree; transformationangle=pi; } qqq=2; } else if (cta <= pi/2&&cta>0){ //1 quadrant ctaacute=cta; transformationangle=0; Axtexty=-0.7; Axtextx = Ax/2; Aytextx= -1; Aytexty= Ay/1.2; angledisplayx=Math.cos(cta/3); angledisplayy=Math.sin(cta/3) ctadegreeacute=ctadegree; qqq=3; } else if (cta >= pi/2&&cta<=pi){ //2 q need = for acute debree to be zero ctaacute=pi-cta; transformationangle=pi-ctaacute; Axtexty=-1; Axtextx = Ax/2; Aytextx= +0.6; Aytexty= Ay/1.2; angledisplayx=-Math.cos(ctaacute/3); angledisplayy=Math.sin(ctaacute/3) ctadegreeacute=180-ctadegree; qqq=4; } else if (cta <= -pi/2&&cta>=-pi){ //3 quadrant // alert(cta); ctaacute=pi+cta; transformationangle=pi; Axtexty=+0.3; Axtextx = Ax/2; Aytextx= +1; Aytexty= Ay/1.2; angledisplayx=-Math.cos(ctaacute/3); angledisplayy=-Math.sin(ctaacute/3) ctadegreeacute=180+ctadegree; qqq=5; } else if (cta >= -pi/2&&cta<0){ //4 q ctaacute=cta; transformationangle=0; Axtexty=+0.3; Axtextx = Ax/2; Aytextx= -1; Aytexty= Ay/1.2; angledisplayx=Math.cos(cta/3); angledisplayy=Math.sin(cta/3); ctadegreeacute=-ctadegree; qqq=6; } ]]> CODE_EDITOR angle true false CODE_EDITOR axes true false CODE_EDITOR axaymove false false =xmax) { Axmove = -1; } if ( Ax<=xmin) { Axmove = 1; } if ( Ay>=ymax) { Aymove = -1; } if ( Ay<=ymin) { Aymove = 1; } ]]> CODE_EDITOR quiz false false 0.05&&Math.abs(enterAy-Ay)>0.05){ // better solution 20170707 K1fcorrect = "The correct answer is Ax ="+Ax.toFixed(1)+" and Ay = "+ Ay.toFixed(1) ; //alert(K1fcorrect); score=score; K1fcorrectbackground = "rgba(0,255,0,255)"; //quiz again } } ]]> LIBRARY_EDITOR Lib Page true false LIBRARY_EDITOR quiz true false LIBRARY_EDITOR android true false -1; //&& ua.indexOf("mobile"); } ]]> LIBRARY_EDITOR changeOrientation true false HTML_VIEW_EDITOR HtmlView Page true false 0 2560 0 800 600 true true Elements.Panel true Elements.Panel false Elements.PlottingPanel false Elements.Group2D Elements.Text2D Elements.Text2D Elements.Polygon2D Elements.Polygon2D Elements.Image2D Elements.Text2D Elements.Arrow2D Elements.Text2D Elements.Arrow2D Elements.Segment2D Elements.Arrow2D Elements.Shape2D Elements.Segment2D Elements.Arrow2D Elements.Text2D Elements.Segment2D Elements.Text2D Elements.Arrow2D Elements.Segment2D false Elements.Group2D Elements.Arrow2D false Elements.Group2D Elements.Arrow2D false Elements.Group2D Elements.Arrow2D false Elements.Group2D Elements.Arrow2D Elements.Shape2D true Elements.Panel Elements.ComboBox 0)? opts[0]:""; // selected option if (selected[0]==="Random"){ dt = 0; Axcomponentmove=0; Aycomponentmove=0; } //"x component is parallel to x-axis","y component is parallel to y-axis" else if (option=="x component is parallel to x-axis"){ dt = 0.05; Axcomponentmove=1; Aycomponentmove=0; _play(); text="playing"; } else if (option=="y component is parallel to y-axis"){ dt = 0.05; Axcomponentmove=0; Aycomponentmove=1; _play(); text="playing"; } else if (option=="vector Ax =2,Ay=4"){ dt = 0; Ax=2; Ay=4; Axtext=Ax/2; Aytext=Ay/2; } else if (option=="vector Ax =4,Ay=2"){ dt = 0; Ax=4; Ay=2; Axtext=Ax/2; Aytext=Ay/2; } else if (option=="vector Ax =-4,Ay=2"){ dt = 0; Ax=-4; Ay=2; Axtext=Ax/2; Aytext=Ay/2; } else if (option=="vector Ax =-4,Ay=-2"){ dt = 0; Ax=-4; Ay=-2; Axtext=Ax/2; Aytext=Ay/2; } else if (option=="vector Ax =-2,Ay=-4"){ dt = 0; Ax=-2; Ay=-4; Axtext=Ax/2; Aytext=Ay/2; } else if (option=="vector Ax =-4,Ay=-2"){ dt = 0; Ax=-4; Ay=-2; Axtext=Ax/2; Aytext=Ay/2; } else if (option=="vector Ax =4,Ay=-2"){ dt = 0; Ax=4; Ay=-2; Axtext=Ax/2; Aytext=Ay/2; } else if (option=="magnitude |A| =√(Ax*Ax+Ay*Ay)"){ dt = 0; showComponentsx = true; showComponentsy = true; Axtext=Ax/2; Aytext=Ay/2; } //"equivalent vectors","opposite vectors" else if (option=="equivalent vectors, same magnitude and direction"){ dt = 0.05; _play(); text="playing"; } else if (option=="opposite vectors, same magnitude opposite direction"){ dt = 0.05; _play(); text="playing"; } else if (option=="parallel vectors, same gradient"){ dt = 0.05; _play(); text="playing"; } else if (option=="collinear vectors, lies on the same line"){ dt = 0.05; _play(); text="playing"; } ]]> Elements.TwoStateButton 0]]> Elements.Button 0]]> Elements.Button true Elements.Panel true Elements.Panel true Elements.Panel Elements.Label true Elements.Panel Elements.Slider false Elements.Panel false Elements.Panel Elements.Label false Elements.Panel Elements.Slider Elements.Button 0.05&&Math.abs(enterAy-Ay)>0.05){ // better solution 20170707 K1fcorrect = "The correct answer is Ax ="+Ax.toFixed(1)+" and Ay = "+ Ay.toFixed(1) ; //alert(K1fcorrect); score=score; K1fcorrectbackground = "rgba(0,255,0,255)"; //quiz again debug=2; //debug } } //_initialize(); ]]>