Cleaning

projects/projectile/index.html

@@ -34,17 +34,19 @@
 <br /><br /><br />
 
 <h3>Projectile Motion</h3>
-<p>To determine to position of the projectile we should compute the position vector \(\vec{r}(t)=x(t)\vec{i}+y(t)\vec{i}\).</p>
+<p>To determine to position of the projectile we should compute the position vector \(\vec{r}(t)=x(t)\vec{i}+y(t)\vec{j}\).</p>
 <h5>\(x(t)\):</h5>
 <p>We know from Newton second law that \(\sum \vec{F} = m\times \vec{a}_x = m\times a_x(t)\vec{i}\)</p>
 <p>However, the projectile as a constant speed along \(\vec{i}\). Hence, \(a_x(t) = 0 \).</p>
 <p>Thus:</p>
+\[ v_x(t) = v_{x,0} \]
 \[ x(t) = \int_{t_0}^t v_{0,x}dt = v_{0,x}t + C = v_{0,x}t + x_0\]
 <h5>\(y(t)\):</h5>
-<p>We know from Newton second law that \(\sum \vec{F} = m\times \vec{a}_y = m\times a_y(t)\vec{i}\)</p>
+<p>We know from Newton second law that \(\sum \vec{F} = m\times \vec{a}_y = m\times a_y(t)\vec{j}\)</p>
 <p>The projectile is under the influence of the gravity that is oriented <em>downward</em>. Hence, \(a_y(t) = -g \).</p>
 <p>Thus:</p>
 \[ v_y(t) = \int_{t_0}^t a_{y}(t)dt = -gt+C = -gt + v_{0,y}\]
 \[ y(t) = \int_{t_0}^t v_y(t)dt = -\frac{1}{2}gt^2 + v_{0,y}t+C=-\frac{1}{2}gt^2 + v_{0,y}t+y_0\]
 <h5>\(\vec{r}(t)\):</h5>
-Finally knowing \(x(t)\) and \(y(t)\) we have \( \vec{r}(t) = \left(\begin{smallmatrix}x(t)\\y(t)\end{smallmatrix}\right) = \left(\begin{smallmatrix}v_{0,x}t + x_0\\-\frac{1}{2}gt^2 + v_{0,y}t+y_0\end{smallmatrix}\right)\)
+<p>Finally knowing \(x(t)\) and \(y(t)\) we have \( \vec{r}(t) = \left(\begin{smallmatrix}x(t)\\y(t)\end{smallmatrix}\right) = \left(\begin{smallmatrix}v_{0,x}t + x_0\\-\frac{1}{2}gt^2 + v_{0,y}t+y_0\end{smallmatrix}\right)\)</p>
+<p>We can deduce also that \( \vec{v}(t) = \left(\begin{smallmatrix}v_x(t)\\v_y(t)\end{smallmatrix}\right) = \left(\begin{smallmatrix}v_{0,x}\\-gt+v_{0,y}\end{smallmatrix}\right)\)</p>

projects/projectile/index.js

@@ -23,6 +23,13 @@ let projectile= function (p){
         vt=p.createElement('span', '');
         katex.render("v(t)", vt.elt);
 
+        vi=p.createElement('span', '');
+        katex.render("\\vec{i}", vi.elt);
+
+        vj=p.createElement('span', '');
+        katex.render("\\vec{j}", vj.elt);
+
+        
     };
 
     // See explanations
@@ -35,7 +42,7 @@ let projectile= function (p){
     }
 
     function v(t) {
-        return (-g * t + v0)
+        return -g * t + v0
     }
 
     let draw_vectors=function(x,y,skiparrow=false){
@@ -44,8 +51,14 @@ let projectile= function (p){
         draw_arrow(p,x,y,x+x0,y-v(t),vt,c,skiparrow)
         p.stroke(200)
         draw_arrow(p,x0,height-y0,x,y,r,c,skiparrow)
-        p.stroke(122, 199, 107)
+        p.stroke(181, 107, 199)
         draw_arrow(p,x0,height-y0,x0+v0,height-(y0+v0),v0t,c,skiparrow)
+
+        p.stroke(121, 199, 107)
+        draw_arrow(p,50,50,50,0,vj,c,skiparrow,true)
+        p.stroke(199,119,107)
+        draw_arrow(p,50,50,100,50,vi,c,skiparrow)
+
         p.pop()
     }
     
@@ -72,6 +85,7 @@ let projectile= function (p){
               end=true
         }
 
+        // Update state
         if(!end){
             t+=0.1
             dots.push([x,y])
@@ -89,7 +103,6 @@ refresh=function(){
     y0=parseFloat(app.y0)
     v0=parseFloat(app.v0)
     g=parseFloat(app.g)
-    console.log(app.x0)
     p5Load()
 }
 

public/js/p5_custom.js

@@ -1,5 +1,5 @@
 
-draw_arrow=function(p,x1,y1,x2,y2,elt=null,canvas,skiparrow=false){
+draw_arrow=function(p,x1,y1,x2,y2,elt=null,canvas,skiparrow=false,flip=false){
     var offset=5
     
     // Reduce the length of the vector to have a better tip location
@@ -30,6 +30,12 @@ draw_arrow=function(p,x1,y1,x2,y2,elt=null,canvas,skiparrow=false){
         xfactor=1-yfactor
         justify=15
 
+        if(flip){
+            xfactor=-xfactor
+            yfactor=-yfactor
+        }
+            
+        
         if(angle>0){
             yfactor=-yfactor
         }