projectile tweaks

draw.js

@@ -324,6 +324,16 @@ class Drawing {
       this.ctx.stroke();
     })
   }
+
+  text(p, text, opts) {
+    this.sequence.push(() => {
+      const [x, y] = this.pixel(this.getPoint(p));
+      this.ctx.font = "12pt sans-serif";
+      this.ctx.textAlign = opts?.align ?? 'left';
+      this.ctx.textBaseline = opts?.baseline ?? 'bottom';
+      this.ctx.fillText(text, x, y);
+    });
+  }
   
   static fromText(node) {
     const div = document.createElement('div');

test.md

@@ -70,21 +70,44 @@ func Math.sin(x + 2*Math.PI*_.t / 1000)
 start
 ``` 
 
+
 ---
 
-## Slide 5
+## Slide 4
 
 ```drawing
+title Sine * Cosine
+caption `y = sin(x) * cos(x)`
+scale 64
+frame 0 -1 2*Math.PI 1
+stroke black 4
+eval _.line([0, -1], [0, 1])
+eval _.line([0, 0], [2*Math.PI, 0])
+stroke red 1
+func Math.sin(x)
+stroke blue 1
+func Math.cos(x)
+stroke purple 2
+func Math.sin(x) * Math.cos(x)
+start
+``` 
+
+---
+
+```drawing
+scale 2
 title Projectile
 caption `x = v_(0x) t`<br>`y = v_(0y) t - g t^2`
-scale 2
+frame -10 -50 300 80
-frame 0 -50 300 100
 stroke black 4
 eval _.polyline([0, 100], [0, 0], [300, 0]);
 value v0 50
-value angle Math.PI / 4
+value angle Math.PI / 180 * 45;
+fill green
+eval _.text([10, 0], '45°')
 value v0x _.getValue('v0') * Math.cos(_.getValue('angle'))
 value v0y _.getValue('v0') * Math.sin(_.getValue('angle'))
+eval _.text([_.getValue('v0x') / 2, _.getValue('v0y') / 2], `${_.getValue('v0')} m/s`, {align: 'right'});
 point p1 (function() {
   const t = _.t / 1000;
   const v0x = _.getValue('v0x');
@@ -107,6 +130,7 @@ point p1 (function() {
     _.arrow([x, y], [x + v0x, y + vy]);
     _.stop();
     _.t = 0;
+    _.text([x, y + 10], `x = ${Math.ceil(x)} m`);
     return [0, 0];
   }
   return [x, y];
@@ -124,10 +148,146 @@ point p2 (function() {
   const p2 = r.add(v);
   return p2.array; 
  })()
-stroke green 2
-eval _.arrow([0, 0], [_.getValue('v0x'), _.getValue('v0y')])
 stroke orange 2
 eval _.arrow('p1', 'p2');
+stroke green 2
+eval _.arrow([0, 0], [_.getValue('v0x'), _.getValue('v0y')])
+fill blue
+eval const projectile = d.circle('p1', {trace: {age: -1}});
+  d.onStart(() => {
+    if (d.t == 0) {
+      projectile.reset();
+    }
+  })
+start
+``` 
+
+---
+
+### 45° ± 15°
+
+```drawing
+scale 2
+frame -10 -50 300 80
+stroke black 4
+eval _.polyline([0, 100], [0, 0], [300, 0]);
+value v0 50
+value angle Math.PI / 180 * 30;
+fill green
+eval _.text([20, 0], '30°')
+value v0x _.getValue('v0') * Math.cos(_.getValue('angle'))
+value v0y _.getValue('v0') * Math.sin(_.getValue('angle'))
+eval _.text([_.getValue('v0x') / 2, _.getValue('v0y') / 2], `${_.getValue('v0')} m/s`, {align: 'right'});
+point p1 (function() {
+  const t = _.t / 1000;
+  const v0x = _.getValue('v0x');
+  const v0y = _.getValue('v0y');
+  const g = 9.81;
+  const x = v0x * t;
+  const y = v0y * t - g * t**2 / 2;
+  const vy = v0y - g * t;
+  const vyp = v0y - g * (t - _.dt/1000);
+  if (vy < 0 && vyp >= 0) {
+    _.setFill('red');
+    _.circle([x, y]);
+    _.setStroke('green', 2);
+    _.arrow([x, y], [x + v0x, y + vy]);
+  }
+  if (t > 0 && (y <= 0 || x >= _.frame[1][0])) {
+    _.setFill('red');
+    _.circle([x, y]);
+    _.setStroke('green', 2);
+    _.arrow([x, y], [x + v0x, y + vy]);
+    _.stop();
+    _.t = 0;
+    _.text([x, y + 10], `x = ${Math.ceil(x)} m`);
+    return [0, 0];
+  }
+  return [x, y];
+ })()
+point p2 (function() {
+  const t = _.t / 1000;
+  const v0x = _.getValue('v0x');
+  const v0y = _.getValue('v0y');
+  const g = 9.81;
+  const x = v0x * t;
+  const y = v0y * t - g * t**2 / 2;
+  const vy = v0y - g * t;
+  const v = new Vector([v0x, vy]);
+  const r = new Vector([x, y]);
+  const p2 = r.add(v);
+  return p2.array; 
+ })()
+stroke orange 2
+eval _.arrow('p1', 'p2');
+stroke green 2
+eval _.arrow([0, 0], [_.getValue('v0x'), _.getValue('v0y')])
+fill blue
+eval const projectile = d.circle('p1', {trace: {age: -1}});
+  d.onStart(() => {
+    if (d.t == 0) {
+      projectile.reset();
+    }
+  })
+start
+``` 
+
+```drawing
+scale 2
+frame -10 -50 300 100
+stroke black 4
+eval _.polyline([0, 100], [0, 0], [300, 0]);
+value v0 50
+value angle Math.PI / 180 * 60;
+fill green
+eval _.text([10, 0], '60°')
+value v0x _.getValue('v0') * Math.cos(_.getValue('angle'))
+value v0y _.getValue('v0') * Math.sin(_.getValue('angle'))
+eval _.text([_.getValue('v0x') / 2, _.getValue('v0y') / 2], `${_.getValue('v0')} m/s`, {align: 'right'});
+point p1 (function() {
+  const t = _.t / 1000;
+  const v0x = _.getValue('v0x');
+  const v0y = _.getValue('v0y');
+  const g = 9.81;
+  const x = v0x * t;
+  const y = v0y * t - g * t**2 / 2;
+  const vy = v0y - g * t;
+  const vyp = v0y - g * (t - _.dt/1000);
+  if (vy < 0 && vyp >= 0) {
+    _.setFill('red');
+    _.circle([x, y]);
+    _.setStroke('green', 2);
+    _.arrow([x, y], [x + v0x, y + vy]);
+  }
+  if (t > 0 && (y <= 0 || x >= _.frame[1][0])) {
+    _.setFill('red');
+    _.circle([x, y]);
+    _.setStroke('green', 2);
+    _.arrow([x, y], [x + v0x, y + vy]);
+    _.stop();
+    _.t = 0;
+    _.text([x, y + 10], `x = ${Math.ceil(x)} m`);
+    return [0, 0];
+  }
+  return [x, y];
+ })()
+point p2 (function() {
+  const t = _.t / 1000;
+  const v0x = _.getValue('v0x');
+  const v0y = _.getValue('v0y');
+  const g = 9.81;
+  const x = v0x * t;
+  const y = v0y * t - g * t**2 / 2;
+  const vy = v0y - g * t;
+  const v = new Vector([v0x, vy]);
+  const r = new Vector([x, y]);
+  const p2 = r.add(v);
+  return p2.array; 
+ })()
+stroke orange 2
+eval _.arrow('p1', 'p2');
+stroke green 2
+eval _.arrow([0, 0], [_.getValue('v0x'), _.getValue('v0y')])
 fill blue
 eval const projectile = d.circle('p1', {trace: {age: -1}});
   d.onStart(() => {