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Loic Guegan 2021-10-04 17:53:12 +02:00
parent a31149727b
commit 83f94fb969
3 changed files with 23 additions and 12 deletions
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15
projects/projectile/index.html
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@ -15,7 +15,7 @@
</div> </div>
<div class="col-sm"> <div class="col-sm">
<div class="input-group"> <div class="input-group">
<div class="input-group-text">\(v_0\)</div> <div class="input-group-text">\(v_{0,x},v_{0,y}\)</div>
<input type="number" class="form-control" v-model="v0" value="50"> <input type="number" class="form-control" v-model="v0" value="50">
<div class="input-group-text">\(m.s\)</div> <div class="input-group-text">\(m.s\)</div>
</div> </div>
@ -34,4 +34,15 @@
<br /><br /><br /> <br /><br /><br />
<h3>Projectile Motion</h3> <h3>Projectile Motion</h3>
\[ \int_{0}^{10} \frac{56}{875} \] <p>To determine to position of the projectile we should compute the position vector \(\vec{r}=x(t)\vec{i}+y(t)\vec{i}\).</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>
\[ x(t) = \int_{t_0}^t v_{0,x}dt = v_{0,x}t + C = v_{0,x}t + x_0\]
<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>The projectile is under the influence of the gravity that is oriented <em>downwarde</em>. Hence, \(a_y(t) = -g \).</p>
<p>Thus:</p>
\[ v_y(t) = \int_{t_0}^t a_{y}(t)dt = -gt+C = -gt + v_{0,y}\]
\[ y(t) = \int_{t_0}^t v_y(t)dt = -\frac{1}{2}gt^2 + v_{0,y}t+C=-\frac{1}{2}gt^2 + v_{0,y}t+y_0\]

14
projects/projectile/index.js
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@ -6,19 +6,18 @@ let y0=50
let g=9.81 let g=9.81
let projectile= function (node){ let projectile= function (node){
let width=800
let height=300
let dots=[] // Dots that show projectile path
node.setup = function() { node.setup = function() {
c=node.createCanvas(width, height); c=node.createCanvas(width, height);
v0t=node.createElement('p', ''); v0t=node.createElement('p', '');
katex.render("v_0", v0t.elt); katex.render("v_0", v0t.elt);
v0t.elt.style.color="#b4b4b4" v0t.elt.style.color="#b4b4b4"
}; };
let width=800
let height=300
// See explanations
let dots=[]
function x(t) { function x(t) {
return x0+v0*t return x0+v0*t
} }
@ -27,6 +26,7 @@ let projectile= function (node){
return height - (-1/2 * g * t**2 + v0 * t + y0) return height - (-1/2 * g * t**2 + v0 * t + y0)
} }
node.draw = function() { node.draw = function() {
node.background(70); node.background(70);
node.noStroke(); node.noStroke();
@ -47,8 +47,10 @@ let projectile= function (node){
v0t.position(c.position().x+m.x,c.position().y+m.y) v0t.position(c.position().x+m.x,c.position().y+m.y)
node.pop() node.pop()
}; };
node.windowResized = function(){ node.windowResized = function(){
v0t.position(c.position().x+m.x,c.position().y+m.y) v0t.position(c.position().x+m.x,c.position().y+m.y)
node.resizeCanvas(Math.min(window.innerWidth,width), height);
} }
}; };

6
template.html
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@ -46,10 +46,8 @@
</div> </div>
<br /> <br />
<div class="row"> <div class="row">
<div class="col"> <div class="col" style="padding:0px;">
<center> <div id="canvas" style="margin-bottom:2em" align="center"></div>
<div id="canvas" style="margin-bottom:2em;"></div>
</center>
</div> </div>
</div> </div>
<div class="row"> <div class="row">