{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![En tête general](img/En_tete_general.png)\n",
    "\n",
    "\n",
    "*(C) Copyright Franck CHEVRIER 2019-2020 http://www.python-lycee.com/*\n",
    "\n",
    "<span style=\"color: #9317B4\"> Pour exécuter une saisie Python, sélectionner la cellule et valider avec </span><span style=\"color: #B317B4\"><strong>SHIFT+Entrée</strong></span>.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Base_Ball](img/BaseBall_titre.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <span style=\"color: red\"> (corrigé)</span> \n",
    "\n",
    "Dans cette activité, on observe à l'aide d'un appareil photographique à déclenchement en rafale la trajectoire d'une balle lancée par un joueur de Baseball. Ceci permet d'obtenir des images de la scène à intervalle de temps constant.\n",
    "\n",
    "L'animation ci-dessous permet d'obtenir de cette façon une <a href=\"https://fr.wikipedia.org/wiki/Chronophotographie\">chronophotographie</a> de ce lancer. Les distances et les temps sont respectivement exprimés en mètre et en seconde.\n",
    "\n",
    "\n",
    "<span style=\"color: #FF0000\">Pour faire apparaître et activer l'animation, sélectionner la cellule ci-dessous et valider avec <strong>SHIFT+Entrée</strong>.</span>\n",
    "\n",
    "\n",
    "<span style=\"color: #BDBFBF\">Vous pouvez ensuite utiliser les menus cinématiques :</span>\n",
    "\n",
    "\n",
    "![Menus_animation](img/menus_animation_GeoGebra.png)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "fig_dyn_GeoGebra/Base_Ball.html"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Sélectionner cette zone puis SHIFT+ENTREE\n",
    "from IPython.display import display, HTML ; display(HTML('fig_dyn_GeoGebra/Base_Ball.html'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__1. Compléter les saisies ci dessous pour stocker les valeurs des abscisses et des ordonnées obtenues par ce pointage dans les listes Python nommées <mark>x</mark> et <mark>y</mark>. Vérifier que la valeur <mark>Dt</mark> correspond bien à l'intervalle de temps $\\Delta t$ paramétré dans votre pointage.__\n",
    "\n",
    "<span style=\"color: #A9AAAA\">Ne pas oublier de valider cette zone de saisie Python et les suivantes avec <strong>SHIFT+Entrée</strong>.</span>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#liste des abscisses des points (à compléter)\n",
    "x = [0,2.68,5.36,8.04,10.72,13.4,16.08,18.75,21.43]\n",
    "\n",
    "#liste des ordonnées des points (à compléter)\n",
    "y = [1.6,3.49,4.99,6.08,6.77,7.07,6.96,6.45,5.55]\n",
    "\n",
    "#intervalle de temps entre deux prises de vue\n",
    "Dt = 0.2 \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__2. Pour chaque point $M_i(x_i;y_i)$, on fait l'estimation que les coordonnées du vecteur vitesse $\\vec{v_i}$ vérifient :__\n",
    "  \n",
    "  \n",
    "<font size=\"3\"> $\\displaystyle \\left( \\vec{v_i} \\right)_x = \\frac{x_{i+1}-x_i}{Δt}$ </font>  <strong>et</strong>\n",
    " \n",
    "<font size=\"3\"> $\\displaystyle \\left( \\vec{v_i} \\right)_y = \\frac{y_{i+1}-y_i}{Δt}$ </font>.\n",
    "\n",
    "__On a défini ci-dessous la liste <mark>vx</mark> des abscisses de ces vecteurs. Définir de la même façon la liste <mark>vy</mark> de leurs ordonnées.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# liste des abscisses des vecteurs vitesse\n",
    "vx = [ (x[i+1]-x[i])/Dt for i in range(len(x)-1) ]\n",
    "\n",
    "# liste des ordonnées des vecteurs vitesse (à créer)\n",
    "vy = [ (y[i+1]-y[i])/Dt for i in range(len(y)-1) ]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__3. En chaque point $M_{i+1}$, on définit le vecteur variation de vitesse $ \\overrightarrow{ \\Delta v }_{ i \\rightarrow i+1 }$ dont les coordonnées vérifient:__\n",
    "  \n",
    "  \n",
    "<font size=\"3\"> $ \\left( \\overrightarrow{  \\Delta v }_{ i \\rightarrow i+1 } \\right)_x = \\left( \\overrightarrow{v_{i+1}} \\right)_x- \\left(\\vec{v_i} \\right)_x$ </font>   <strong>et</strong>    \n",
    " \n",
    "<font size=\"3\"> $ \\left( \\overrightarrow{  \\Delta v }_{ i \\rightarrow i+1 } \\right)_y = \\left( \\overrightarrow{v_{i+1}} \\right)_y- \\left(\\vec{v_i} \\right)_y$ </font>.  \n",
    " \n",
    "__On a défini ci-dessous la liste <mark>Dvx</mark> des abscisses de ces vecteurs. Définir de la même façon la liste <mark>Dvy</mark> de leurs ordonnées.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# liste des abscisses des vecteurs variation de vitesse\n",
    "Dvx = [ vx[i+1]-vx[i] for i in range(len(vx)-1) ]\n",
    "\n",
    "# liste des ordonnées des vecteurs variation vitesse (à créer)\n",
    "Dvy = [ vy[i+1]-vy[i] for i in range(len(vy)-1) ]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__4. La fonction Python <mark>Pointage</mark> ci-dessous permet d'obtenir le tracé des <span style=\"color: #0000FF\">vecteurs vitesse</span> et des <span style=\"color: #FF7711\">vecteurs variation de vitesse</span> pour le <span style=\"color: #FF0000\">pointage</span>. Exécuter cette cellule et la suivante pour observer le graphique.__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Exécuter cette cellule\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def Pointage():\n",
    "    \n",
    "    # réglage des axes\n",
    "    plt.figure(num=0, figsize=(12,8), dpi=80) ; fig,ax = plt.subplots(num=0)  \n",
    "    ax.set_xlim(( 0,max(x[i]+vx[i]+0.5 for i in range(len(vx))))) ; ax.set_ylim((0,max(y[i]+vy[i]+0.5 for i in range(len(vy))))) ;\n",
    "        \n",
    "    # représentation des points\n",
    "    plt.scatter(x,y,color='red') \n",
    "    \n",
    "    # représentation des vecteurs vitesse\n",
    "    for i in range(len(vx)):\n",
    "        plt.arrow( x[i] , y[i] , vx[i] , vy[i] , head_width=0.2, head_length=0.2, fc='lightblue', ec='blue')\n",
    "        \n",
    "    # représentation des vecteurs variation de vitesse     \n",
    "    for i in range(len(Dvx)):\n",
    "        plt.arrow( x[i+1] , y[i+1] , Dvx[i] , Dvy[i] , head_width=0.2, head_length=0.2, fc='coral', ec='orangered')\n",
    "    \n",
    "    # affichage\n",
    "    plt.show()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2d06d89b470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Exécuter cette cellule pour appeler la fonction Pointage\n",
    "Pointage()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__5. a. A l'aide du graphique obtenu et des résultats des deux saisies Python suivantes, justifier que le vecteur variation de vitesse peut être considéré comme constant, et préciser une valeur approchée de sa norme.__\n",
    "\n",
    "<span style=\"color: red\"> D'après le graphique et les valeurs obtenues, il semble que les vecteurs variation de vitesse sont tous verticaux, orientés vers le bas et égaux, de norme environ $2$ (ce qui correspond donc à une variation de vitesse de $2$ $\\mathrm{m} \\cdot \\mathrm{s}^{-1}$ sur chaque intervalle de temps de durée $\\Delta t$). </span> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.0,\n",
       " -7.105427357601002e-15,\n",
       " 1.4210854715202004e-14,\n",
       " -8.881784197001252e-15,\n",
       " -8.881784197001252e-15,\n",
       " -0.04999999999998117,\n",
       " 0.04999999999999005]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Exécuter cette cellule\n",
    "Dvx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-1.9499999999999993,\n",
       " -2.0500000000000007,\n",
       " -2.0000000000000018,\n",
       " -1.949999999999994,\n",
       " -2.050000000000005,\n",
       " -1.9999999999999973,\n",
       " -1.9500000000000028]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Exécuter cette cellule\n",
    "Dvy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__5. b. On admet que la balle de Baseball a une masse de $145$ $\\mathrm{g}$.__ \n",
    "\n",
    "__A l'aide d'une saisie Python, déterminer l'intensité du poids exercé sur cette balle.__\n",
    "\n",
    "On prendra $g=10$ $\\mathrm{N} \\cdot \\mathrm{kg}^{-1}$ pour l'intensité de la pesanteur.\n",
    "\n",
    "<span style=\"color: red\"> $P=mg=145 \\times 10^{-3} \\times 10=1,45$ $\\mathrm{N}$</span>\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.45"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Effectuer ici la saisie nécessaire pour déterminer l'intensité du poids\n",
    "145*10**-3*10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__5.c A l'aide de l'égalité $\\displaystyle \\sum{ \\vec{F}}=m \\; \\frac{\\overrightarrow{\\Delta v}}{\\Delta t}$, justifier qu'on peut considérer que seule la force du vecteur poids s'applique sur la balle.__ \n",
    "\n",
    "__Que peut-on en déduire concernant le mouvement de la balle ?__\n",
    "\n",
    "On pourra utiliser la cellule ci-dessous pour effectuer les calculs utiles.\n",
    "\n",
    "<span style=\"color: red\"> $\\displaystyle \\sum{ \\vec{F}}=m \\; \\frac{\\overrightarrow{\\Delta v}}{\\Delta t}$ a pour intensité $145 \\times 10^{-3} \\times \\frac{2}{0,2} =1,45$ $\\mathrm{N}$, et on retrouve l'intensité du poids. </span>\n",
    "\n",
    "<span style=\"color: red\">Seul le poids s'applique à la balle et on peut donc considérer que celle-ci est en chute libre. </span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4499999999999997"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Effectuer ici les calculs utiles\n",
    "145*10**-3*2/0.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__6. Reprendre les questions précédentes pour un autre pointage, obtenu avec d'autres valeurs pour les paramètres $h_0$ (hauteur initiale), $v_0$ (vitesse initiale) et $\\alpha$ (angle du lancer par rapport à l'horizontale).__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*(C) Copyright Franck CHEVRIER 2019-2020 http://www.python-lycee.com/*\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:#AA00AA\">*Remerciements particuliers à Nicolas EHRSAM pour son aide précieuse.*</span>"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Raw Cell Format",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}