notebooks/01-soccer-ball.ipynb

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    "# Notebook 1: ⚽ Goal! Analyzing a Soccer Kick 🥅\r\n",
    "\r\n",
    "---\r\n",
    "\r\n",
    "## 👋 Hey Maddie, Back to Where We Started! ✨\r\n",
    "\r\n",
    "Remember that first soccer ball kick we looked at? Now we're going to break down a similar problem from your worksheet, step-by-step, using everything we've learned! It's the same awesome parabola math.\r\n",
    "\r\n",
    "Let's analyze this soccer kick:\r\n",
    "\r\n",
    "- ✅ Find out **how long** it takes the ball to reach its highest point.\r\n",
    "- ✅ Calculate the **maximum height** the ball reaches.\r\n",
    "- ✅ Figure out **how long the ball is in the air** before it lands.\r\n",
    "- ✅ **Draw and label a sketch** showing the ball's path.\r\n",
    "\r\n",
    "Ready to score this math goal? Let's kick it off! ⚽️💨"
   ]
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    "---\r\n",
    "\r\n",
    "## 📝 Game Plan: What Do We Know About the Kick? 🤔\r\n",
    "\r\n",
    "Let's grab the key details from Question 1:\r\n",
    "\r\n",
    "> A soccer player kicks a ball with an **initial velocity of 32 ft/sec**.\r\n",
    "> It's kicked from a **starting height of 0 feet** (right off the ground).\r\n",
    "\r\n",
    "*(We'll put the picture of the actual worksheet question in the next cell!)*\r\n",
    "\r\n",
    "Time to use our trusty formula...\r\n",
    "\r\n",
    "---"
   ]
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    "![Question 1 Worksheet](../images/question-1.png)\r\n",
    "\r\n",
    "---"
   ]
  },
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    "## ✨ The Height Formula for This Kick! ✨\r\n",
    "\r\n",
    "It's the same amazing formula as always, tracking the height (h) at any time (t):\r\n",
    "\r\n",
    "\\\\[ h(t) = -16t^2 + vt + h_0 \\\\]\r\n",
    "\r\n",
    "Let's plug in the numbers for *this specific soccer kick*:\r\n",
    "\r\n",
    "- **v** (initial velocity) = **32 ft/s** (How fast it was kicked upwards)\r\n",
    "  *(That's about 22 mph - a decent kick!)*\r\n",
    "- **h₀** (starting height) = **0 ft** (It started on the ground)\r\n",
    "- **-16** is **gravity** pulling it back down. 🌎\r\n",
    "\r\n",
    "So, our formula simplifies nicely because h₀ is 0:\r\n",
    "\r\n",
    "\\\\[ h(t) = -16t^2 + 32t + 0 \\\\]\r\n",
    "or just\r\n",
    "\\\\[ h(t) = -16t^2 + 32t \\\\]\r\n",
    "\r\n",
    "Now we have the exact equation for this ball's flight! Let's solve the questions. 💪\r\n",
    "\r\n",
    "---"
   ]
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    "## ⏰ Step 1 (Part a): Up, Up, Up! Time to Reach the Peak ⚽️\r\n",
    "\r\n",
    "**Why find the peak time?** 🤔 The ball goes up, hangs for a split second at its highest point (the **vertex**), and then comes back down. The first question asks *when* it reaches that highest point.\r\n",
    "\r\n",
    "We use our shortcut formula for finding the time to the peak:\r\n",
    "\r\n",
    "> **Time = -velocity ÷ (2 × gravity's coefficient)**\r\n",
    "\r\n",
    "Let's plug in the numbers for *this* soccer kick:\r\n",
    "- **velocity (v)** = **32 ft/s**\r\n",
    "- **gravity's coefficient (a)** = **-16** (the number multiplying t²)\r\n",
    "\r\n",
    "Let's find the time!"
   ]
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   "source": [
    "Time = -(32) ÷ (2 × -16)"
   ]
  },
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   "source": [
    "Time = -32 ÷ -32"
   ]
  },
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    "Time = 1 second"
   ]
  },
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    "✅ Perfect! The soccer ball reaches its highest point exactly **1 second** after being kicked.\r\n",
    "\r\n",
    "✨ It takes just one second to get to the very top of its flight!\r\n",
    "\r\n",
    "---"
   ]
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   "source": [
    "## 📏 Step 2 (Part b): How High Did It Go? Finding the Max Height! ⬆️\r\n",
    "\r\n",
    "**Why find the maximum height?** 🤷‍♀️ We know the ball reached its peak at **1 second**. Now we need to figure out *how many feet high* it actually got at that moment. This is the ball's **maximum height**.\r\n",
    "\r\n",
    "We take the peak time (1 second) and plug it into our soccer ball height formula: `h(t) = -16t² + 32t`."
   ]
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   "source": [
    "Height = -16 × time² + 32 × time"
   ]
  },
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   "source": [
    "Let's plug in the peak time (t = 1 second):\r\n",
    "\r\n",
    "Height = -16 × (1)² + 32 × (1)"
   ]
  },
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   "source": [
    "Height = -16 × (1) + 32 × (1)"
   ]
  },
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    "Height = 16 feet"
   ]
  },
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    "✅ Got it! The soccer ball reaches a **maximum height of 16 feet**.\r\n",
    "\r\n",
    "✨ That's about the height of a 1½ story house! Pretty good kick from the ground. 🏠\r\n",
    "\r\n",
    "---"
   ]
  },
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   "source": [
    "## ⏳ Step 3 (Part c): Air Time! When Does the Ball Land? ⏱️\r\n",
    "\r\n",
    "**Why find the landing time?** 🤔 The question asks how long the ball is in the air *total*. It starts on the ground (height=0), goes up, comes down, and lands back on the ground (height=0 again). We need to find the time (t) for that second moment when the height is 0.\r\n",
    "\r\n",
    "We use our specific height formula `h(t) = -16t² + 32t` and set h(t) = 0."
   ]
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    "Set the height to 0:\r\n",
    "\r\n",
    "`0 = -16t² + 32t`"
   ]
  },
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    "This time, we don't *need* the big quadratic formula because there's no constant term (the 'c' part is zero since h₀=0). We can solve this one more easily by **factoring**!\r\n",
    "\r\n",
    "Notice that both `-16t²` and `32t` have `-16t` as a common factor. Let's pull that out:\r\n",
    "\r\n",
    "`0 = -16t (t - 2)`"
   ]
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   "source": [
    "This time, we don't *need* the big quadratic formula because the starting height (`h₀`) was 0. We can solve this one more easily by **factoring**!\r\n",
    "\r\n",
    "Notice that both `-16t²` and `32t` have `t` as a common factor. Let's pull `t` out:\r\n",
    "\r\n",
    "`0 = t (-16t + 32)`\r\n",
    "\r\n",
    "Now, for the whole thing to equal zero, *either* the part outside the parentheses must be zero, *or* the part inside must be zero. This gives us two possible times:"
   ]
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    "**Possibility 1:**\r\n",
    "`t = 0`\r\n",
    "\r\n",
    "**Possibility 2:**\r\n",
    "`-16t + 32 = 0`\r\n",
    "`-16t = -32`\r\n",
    "`t = -32 / -16`\r\n",
    "`t = 2`"
   ]
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    "So we have two times when the height is 0: **t = 0 seconds** and **t = 2 seconds**.\r\n",
    "\r\n",
    "Which one tells us how long it was in the air? 🤔\r\n",
    "- `t = 0` is the moment the ball was *kicked* (it was on the ground).\r\n",
    "- `t = 2` is the moment the ball *lands* back on the ground after its flight.\r\n",
    "\r\n",
    "✅ Therefore, the ball was in the air for a total of **2 seconds**.\r\n",
    "\r\n",
    "✨ *Notice something cool? It took 1 second to go up and 1 second to come back down. When you start and end at the same height (like the ground), the up time equals the down time!*\r\n",
    "\r\n",
    "---"
   ]
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   "source": [
    "## 🎨 Step 4 (Part d): Picture Time! Sketching the Kick ✍️\r\n",
    "\r\n",
    "**Why sketch the path?** 🖼️ Let's see the whole flight of the soccer ball! Plotting the height over time shows us that familiar **parabola** shape. We'll mark the key points: starting on the ground, reaching the peak, and landing back on the ground.\r\n",
    "\r\n",
    "This graph shows the ball's **height** versus **time**."
   ]
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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Time values: Start at 0, go slightly past landing time (2s)\n",
    "# Key times: peak=1s, landing=2s\n",
    "t = np.linspace(0, 2.1, 100) # Go just beyond 2s\n",
    "\n",
    "# Soccer ball height formula: h(t) = -16t² + 32t\n",
    "h = -16 * t**2 + 32 * t\n",
    "\n",
    "# --- Create the Plot ---\n",
    "plt.figure(figsize=(7, 5))\n",
    "plt.plot(t, h, label=\"h(t) = -16t² + 32t\", color='dodgerblue')\n",
    "\n",
    "# --- Plot and Label Key Points ---\n",
    "start_time, start_height = 0, 0\n",
    "peak_time, peak_height = 1, 16\n",
    "land_time, land_height = 2, 0\n",
    "\n",
    "# Starting Point (Ground)\n",
    "plt.plot(start_time, start_height, 'go', markersize=8)\n",
    "plt.text(start_time + 0.05, start_height + 0.5, f\"Kick ({start_time}s, {start_height}ft)\", color='green')\n",
    "\n",
    "# Peak Point\n",
    "plt.plot(peak_time, peak_height, 'ro', markersize=8)\n",
    "plt.text(peak_time, peak_height + 0.5, f\"Peak ({peak_time}s, {peak_height}ft)\", ha='center', color='red')\n",
    "\n",
    "# Landing Point (Ground)\n",
    "plt.plot(land_time, land_height, 'bo', markersize=8)\n",
    "plt.text(land_time - 0.05, land_height + 0.5, f\"Land ({land_time}s, {land_height}ft)\", ha='right', color='blue')\n",
    "\n",
    "# --- Add Titles and Labels ---\n",
    "plt.title(\"Soccer Ball Kick Trajectory\")\n",
    "plt.xlabel(\"Time (seconds)\")\n",
    "plt.ylabel(\"Height (feet)\")\n",
    "\n",
    "# --- Adjust Axes and Grid ---\n",
    "plt.ylim(bottom=-1) # Start y-axis slightly below 0\n",
    "plt.axhline(0, color='green', linewidth=0.8, linestyle='--') # Line for the ground\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "186fffe4-db76-49d5-8572-a8c83bd81f8f",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 🎉 GOOOOAL! Soccer Problem Solved! 🎉\n",
    "\n",
    "Fantastic job, Maddie! You've successfully analyzed this soccer kick from start to finish. Here's the quick summary:\n",
    "\n",
    "- ✅ The ball was kicked from the **ground** (0 feet) with an upward speed of **32 ft/s**.\n",
    "- 🕒 It reached its peak height after **1 second**.\n",
    "- 📏 The maximum height was **16 feet**.\n",
    "- ⏱️ The ball was in the air for a total of **2 seconds** before landing.\n",
    "\n",
    "You've now seen how the same math applies to fireworks, volleyball, cliff jumps, and soccer balls! It's all about using that height formula and understanding the parabola.\n",
    "\n",
    "**The Key Steps (One More Time!):**\n",
    "1.  Find `h₀` (starting height) and `v` (initial velocity).\n",
    "2.  Write the height formula: `h(t) = -16t² + vt + h₀`.\n",
    "3.  Find time to peak: `t = -v / (2 * -16)`.\n",
    "4.  Plug peak time into h(t) for max height.\n",
    "5.  Set h(t) = 0 to find when it hits height zero (use factoring if h₀=0, or quadratic formula otherwise).\n",
    "6.  Plug in any specific time into h(t) to find the height then.\n",
    "\n",
    "You're doing wonderfully. Keep up the great work! 🤩💯"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
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