notebooks/02-firework-rocket.ipynb

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    "# Notebook 2: 🎆 The Firework Rocket Launch\n",
    "\n",
    "---\n",
    "\n",
    "## 🎈 Welcome Back, Maddie! 🎆\n",
    "\n",
    "Today we’re going to explore another super cool math adventure! But this time... it's not a soccer ball — it's a **fireworks rocket** that shoots up into the sky and falls into a lake. 🌊\n",
    "\n",
    "You’re going to learn how to:\n",
    "- ✅ Figure out **how long** the rocket takes to reach its highest point\n",
    "- ✅ Find the **maximum height** it reaches before exploding\n",
    "- ✅ Solve when it **hits the water**\n",
    "- ✅ Use a formula to figure out how high it is **after 1 second**\n",
    "- ✅ Learn how to **draw the path** it takes, like a rainbow in the sky ✨\n",
    "\n",
    "---\n",
    "\n",
    "## 🚀 Mission Briefing: What Info Do We Have? 🤔\n",
    "\n",
    "Let’s look at the question together — this is the exact type of thing you’ll see on your test. Let's make sure you feel totally confident!\n",
    "\n",
    "We’ll also insert the original image of the question here so you can read it like it shows up in your worksheet. (Coming in the next cell!)\n",
    "\n",
    "But first, here’s what the question says, simplified:\n",
    "\n",
    "> A firework is launched from an **80-foot hill** above a lake. It goes up, up, up — and then explodes at the **highest point**. After that, it falls all the way into the lake.\n",
    ">\n",
    "> The rocket is launched **upward at 64 ft/sec**.\n",
    "\n",
    "And now for the magic math part!\n",
    "\n",
    "---\n",
    "\n",
    "## 💎 The Magic Formula (Just Like Last Time!)\n",
    "\n",
    "---\n"
   ]
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    "## ✨ Our Secret Weapon: The Height Formula! ✨\r\n",
    "\r\n",
    "We’ll use this amazing formula again to track how high the rocket goes over time:\r\n",
    "\r\n",
    "\\\\[ h(t) = -16t^2 + vt + h_0 \\\\]\r\n",
    "\r\n",
    "Where:\r\n",
    "- \\\\( t \\\\) = **time in seconds ⏱** (how long the rocket’s been flying)\r\n",
    "- \\\\( v \\\\) = **initial velocity**, or how fast the rocket launches (in this case: 64 ft/s)\r\n",
    "  *(That's shooting upwards at over 40 miles per hour – faster than cars usually drive on city streets! 🚗💨)*\r\n",
    "- \\\\( h_0 \\\\) = **starting height** (here it’s 80 feet because it's launched from a hill)\r\n",
    "  *(That's like launching it from the roof of an 8-story building, or about the height of 4 giraffes stacked up! 🦒🦒🦒🦒)*\r\n",
    "- \\\\( -16 \\\\) = **gravity** pulling it back down (measured in ft/s²)\r\n",
    "\r\n",
    "So for this problem:\r\n",
    "\r\n",
    "\\\\[ h(t) = -16t^2 + 64t + 80 \\\\]\r\n",
    "\r\n",
    "This formula helps us figure out how high the rocket is at **any second**!"
   ]
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   "source": [
    "![Question 2 Worksheet](../images/question-2.png)"
   ]
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    "---\n",
    "\n",
    "## ⏰ Step 1: Time Flies! When Does it Reach the Top? 🚀\n",
    "\n",
    "**Why find the peak time?** 🤔 Before we can figure out *how high* the rocket flies, we first need to know *when* it gets there. Think of it like pausing a video right when the rocket hits the very top of its arc! This special moment is called the **vertex** of the parabola.\r\n",
    "\r\n",
    "Okay, *now* let’s figure out **when** the rocket stops going up and reaches its highest point.\r\n",
    "Think of it like the very **top of the rainbow arc** 🌈 before the rocket starts falling.\r\n",
    "\r\n",
    "We use this simple formula (it's a shortcut just for finding the time to the peak!):\r\n",
    "...\n",
    "\n",
    "> **Time = -velocity ÷ (2 × gravity)**\n",
    "\n",
    "Now let’s plug in the numbers we know:\n",
    "- The rocket was launched **upward at 64 ft/s**\n",
    "- Gravity pulls down with a strength of **-16 ft/s²**\n",
    "\n",
    "So:"
   ]
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   "source": [
    "Time = -64 ÷ (2 × -16)"
   ]
  },
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   "source": [
    "Time = -64 ÷ -32"
   ]
  },
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   "source": [
    "Time = 2 seconds"
   ]
  },
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   "source": [
    "✅ That means the rocket reaches its highest point exactly **2 seconds** after it’s launched. (Super quick! ⚡️)\r\n",
    "\r\n",
    "✨ That’s the moment the rocket *pauses at the top*, just before it starts falling toward the lake."
   ]
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   "source": [
    "---\n",
    "\n",
    "## 📏 Step 2: Reaching New Heights! How High Did it Go? ⛰️\n",
    "\n",
    "**Why find the peak height?** 🤷‍♀️ We know the rocket reaches its highest point *at 2 seconds*, but the firework question also wants to know *how many feet high* that actually is! This is the rocket's **maximum height**.\r\n",
    "\r\n",
    "So, we'll take the time we just found (2 seconds) and plug it back into our main 'Secret Weapon' height formula.\r\n",
    "\r\n",
    "We know the rocket hits its highest point **2 seconds** after launch. Now let’s use our magic height formula to find *how high* it gets at that moment:\r\n",
    "..."
   ]
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   "source": [
    "Height = -16 × time² + velocity × time + starting height"
   ]
  },
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    "\n",
    "Let’s plug in the numbers we know:\n",
    "- Time = 2 seconds ⏱️  \n",
    "- Velocity = 64 ft/s 🧨  \n",
    "- Starting height = 80 ft (because it was launched from the top of a hill!)\n",
    "\n",
    "So we get:"
   ]
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   "source": [
    "Height = -16 × (2)² + 64 × 2 + 80"
   ]
  },
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   "source": [
    "Height = -16 × 4 + 128 + 80"
   ]
  },
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   "source": [
    "Height = -64 + 128 + 80"
   ]
  },
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   "source": [
    "Height = 144 feet"
   ]
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   "source": [
    "\n",
    "✅ That means the rocket reaches a maximum height of **144 feet** above the lake!\n",
    "\n",
    " ✨ Wow! That’s taller than the Statue of Liberty's pedestal! 🗽 It's also like stacking over **9 Maddies** on top of each other! 😄 (Assuming Maddie is about 5 feet tall)\n"
   ]
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   "source": [
    "---\n",
    "\n",
    "## 🌊 Step 3: Splashdown! When Does it Hit the Lake? ⏱️\n",
    "\n",
    "**Why find the splashdown time?** 🌊 The rocket goes up, peaks, and then falls back down... right into the lake! The question asks *when* this happens. Since the lake's surface is our \"ground level\" in this problem, we need to find the time (t) when the rocket's height (h) is exactly **0 feet**.\r\n",
    "\r\n",
    "Now let’s figure out when the rocket hits the water. Again, that means its height is **0 feet**.\r\n",
    "\r\n",
    "We’ll use the same 'Secret Weapon' formula again:\r\n",
    "...\n"
   ]
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   "cell_type": "markdown",
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   "source": [
    "Height = -16 × time² + 64 × time + 80"
   ]
  },
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   "source": [
    "\n",
    "But this time we **set the height to 0** because we’re solving for when the rocket *lands in the lake*:"
   ]
  },
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   "source": [
    "0 = -16t² + 64t + 80"
   ]
  },
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   "source": [
    "\n",
    "To solve this, we’ll use a shortcut calculator or the **quadratic formula** (don’t worry Maddie, we’ll explain!):\n",
    "\n",
    "🧪 The **quadratic formula** helps us solve any equation that looks like this:\n"
   ]
  },
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   "source": [
    "ax² + bx + c = 0"
   ]
  },
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   "source": [
    "\n",
    "The formula is:"
   ]
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   "source": [
    "t = (-b ± √(b² - 4ac)) ÷ (2a)"
   ]
  },
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   "source": [
    "\n",
    "For our rocket problem:\n",
    "- a = -16  \n",
    "- b = 64  \n",
    "- c = 80\n",
    "\n",
    "Plug those into the formula and you get:"
   ]
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   "source": [
    "t = (-64 ± √(64² - 4(-16)(80))) ÷ (2 × -16)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abc59561-1bbf-4173-96f0-49461710ec79",
   "metadata": {},
   "source": [
    "t = (-64 ± √(4096 + 5120)) ÷ -32 "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b90d399-d293-4b7f-90be-051cf626d0c1",
   "metadata": {},
   "source": [
    "t = (-64 ± √9216) ÷ -32"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca4560c8-2330-4a05-87e1-9327161bf9d4",
   "metadata": {},
   "source": [
    "t = (-64 ± 96) ÷ -32"
   ]
  },
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   "id": "54c29682-cb28-4951-89c2-0fa96c870ced",
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   "source": [
    "\n",
    "Now we get two possible answers:"
   ]
  },
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   "source": [
    "t = (32) ÷ -32 = -1 (we throw this one out — can’t have negative time!)"
   ]
  },
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   "source": [
    "t = (-160) ÷ -32 = 5"
   ]
  },
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   "source": [
    "✅ That means the rocket hits the water **5 seconds** after it launches. (The whole flight is over pretty fast!)\r\n",
    "\r\n",
    "💡 *So it flies up for 2 seconds, pauses at the top, and then falls down for 3 more seconds before landing in the lake!*"
   ]
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   "source": [
    "---\n",
    "\n",
    "## 📍 Step 4: Checkpoint! How High After Just 1 Second? ⏱️\n",
    "\n",
    "**Why find the height at 1 second?** 🤔 The question specifically asks us to check the rocket's height at the 1-second mark. Our 'Secret Weapon' formula is perfect for this – it can tell us the height at *any* specific time! We just need to plug in '1' for the time (t).\r\n",
    "\r\n",
    "Let’s figure out how high the rocket is *exactly 1 second* after it's launched.\r\n",
    "\r\n",
    "We’ll use the same height formula again:\r\n",
    "...\n"
   ]
  },
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   "cell_type": "markdown",
   "id": "39dc44f3-b588-499c-8043-3f94385b6926",
   "metadata": {},
   "source": [
    "Height = -16 × time² + velocity × time + starting height"
   ]
  },
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   "source": [
    "\n",
    "We know:\n",
    "- Time = 1 second\n",
    "- Velocity = 64 ft/s\n",
    "- Starting height = 80 ft\n",
    "\n",
    "Let’s plug in:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbaccb7a-e4b2-4654-9b93-47f77ed940e6",
   "metadata": {},
   "source": [
    "Height = -16 × (1)² + 64 × 1 + 80"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9b508f7-de01-4be0-8ea2-9796e5500c78",
   "metadata": {},
   "source": [
    "Height = -16 + 64 + 80"
   ]
  },
  {
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   "source": [
    "Height = 128 feet"
   ]
  },
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   "source": [
    "✅ That means the rocket is **128 feet** in the air just 1 second after liftoff!\r\n",
    "\r\n",
    "🎈 *Whoa! That’s higher than a 12-story building, or about the length of 3 school buses parked end-to-end, but pointed straight up!* 🚌🚌🚌 ��\r\n",
    "Can you imagine zooming that high in just one second?!"
   ]
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   "source": [
    "---\n",
    "\n",
    "## 🖼️ Picture This! The Rocket's Parabola Path 🌈\n",
    "\n",
    "Now that we’ve done all the math step-by-step — let’s look at the **big picture**.  \n",
    "This chart shows the rocket's **height over time**, from liftoff until it splashes down in the lake.\n",
    "\n",
    "- 💚 It **starts** at 80 feet because it was launched from the top of a hill\n",
    "- 🔺 It reaches the **highest point (144 ft)** after **2 seconds**\n",
    "- 📉 Then it falls back down and **hits the water at 5 seconds**\n",
    "- 💙 You can also see how high it is **exactly at 1 second** (128 ft — whoa!)\n",
    "\n",
    "This is a perfect example of a **parabola** — it goes up in a smooth arc, pauses, and comes back down.\n",
    "\n",
    "✨ The curve you see is just math showing off — like a firework making art in the sky! 💥"
   ]
  },
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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Time values from 0 to 5.5 seconds (just past the splashdown)\n",
    "t = np.linspace(0, 5.5, 200)\n",
    "\n",
    "# Rocket height formula: h(t) = -16t² + 64t + 80\n",
    "h = -16 * t**2 + 64 * t + 80\n",
    "\n",
    "# Create the plot\n",
    "plt.figure(figsize=(8, 5))\n",
    "plt.plot(t, h, label=\"h(t) = -16t² + 64t + 80\", color='purple')\n",
    "\n",
    "# Plot and label key points\n",
    "plt.plot(0, 80, 'go')  # Launch point\n",
    "plt.text(0, 82, \"Launch (0s, 80ft)\", color='green')\n",
    "\n",
    "plt.plot(2, 144, 'ro')  # Peak\n",
    "plt.text(2, 146, \"Peak (2s, 144ft)\", ha='center', color='red')\n",
    "\n",
    "plt.plot(5, 0, 'bo')  # Splashdown\n",
    "plt.text(5, 2, \"Splashdown (5s, 0ft)\", color='blue')\n",
    "\n",
    "plt.plot(1, 128, 'co')  # Height at 1s\n",
    "plt.text(1, 130, \"1s = 128ft\", color='cyan')\n",
    "\n",
    "# Add titles and labels\n",
    "plt.title(\"Firework Rocket Flight Path\")\n",
    "plt.xlabel(\"Time (seconds)\")\n",
    "plt.ylabel(\"Height (feet)\")\n",
    "plt.ylim(0, 160)  # This removes negative height from the chart and caps it a bit above the peak\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()"
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    "---\n",
    "\n",
    "## ✨ Wrapping It Up: You're a Rocket Scientist! 🚀\n",
    "\n",
    "Let’s look back and celebrate everything we figured out like rocket scientists 🚀:\n",
    "\n",
    "- ✅ The rocket was launched from **80 feet** high\n",
    "- 🕒 It took **2 seconds** to reach its highest point\n",
    "- 📏 It soared to a **maximum height of 144 feet**\n",
    "- 🕔 It landed **5 seconds** after liftoff (hello splashdown!)\n",
    "- 📍 It reached **128 feet** in the air just **1 second** after launch\n",
    "\n",
    "---\n",
    "\n",
    "✨ **Now imagine this on a test…**\n",
    "You’ll be totally ready! Just remember:\n",
    "- Use the magic formula: `Height = -16t² + vt + h₀`\n",
    "- Pause and ask: what do we already know?\n",
    "- Plug it in step-by-step (like we did in this notebook!)\n",
    "- Visualize it! The path of a rocket is really just a **parabola in disguise** 🧠🌈\n",
    "\n",
    "---\n",
    "\n",
    "💡 **Bonus Questions to Think About**  \n",
    "_(You don’t have to answer these now, but they’re fun to think about!)_\n",
    "- What would happen if the rocket was launched at **80 ft/s instead of 64**?\n",
    "- What if it was launched from the **ground** instead of a hill?\n",
    "- Could we use this same formula for a basketball or a firework or a volleyball?\n",
    "\n",
    "---\n",
    "\n",
    "🧠 You’ve got this, Maddie! Keep practicing, and soon these types of problems will feel like second nature."
   ]
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