[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"public-settings":3,"content:materi:gerak-parabola":11,"public-catalog":214},{"features.tutoring.enabled":4,"sections.subjects.enabled":5,"sections.pricing.enabled":5,"sections.teachers.enabled":5,"sections.testimonials.enabled":4,"sections.faqs.enabled":5,"bankSoal.enabled":5,"site.maintenance":4,"whatsapp.number":6,"brand.name":7,"brand.tagline":8,"contact.email":9,"contact.address":10},false,true,"6285156084435","MyFismat","Platform belajar Matematika, Fisika, dan Pemrograman untuk SD, SMP, SMA, dan Kuliah","support@myfismat.com","Indonesia",{"id":12,"type":13,"slug":14,"title":15,"excerpt":16,"coverUrl":17,"status":18,"publishedAt":19,"featured":4,"subjectId":20,"blocks":21,"seoTitle":17,"seoDescription":17,"readingMinutes":100,"order":101,"createdAt":102,"updatedAt":102,"subject":103,"levels":108,"topics":113,"tags":117,"author":17,"resolved":118,"related":141},"demo-v2-m-fisika-sma-2","MATERIAL","gerak-parabola","Gerak Parabola: Rumus, Tinggi Maksimum, dan Contoh Soal","Rumus gerak parabola: komponen kecepatan, tinggi maksimum, waktu terbang, dan jarak terjauh, dengan simulasi interaktif dan contoh soal kelas 10–11.",null,"PUBLISHED","2026-10-08T23:58:23.324Z","cmuzbyhdq000571r9nsdk6scx",[22,27,34,38,42,46,51,58,62,66,70,76,82,86,90,94],{"id":23,"data":24,"type":26},"s1-1",{"markdown":25},"**Gerak parabola** adalah gerak benda yang dilempar dengan sudut elevasi tertentu sehingga lintasannya melengkung berbentuk parabola. Gerak ini merupakan gabungan **GLB** pada arah mendatar (kecepatan tetap) dan **GLBB** pada arah tegak (percepatan gravitasi ke bawah). Pada materi ini dipakai $g = 9{,}8$ m\u002Fs² dan hambatan udara diabaikan.","text",{"id":28,"data":29,"type":33},"s1-2",{"title":30,"variant":31,"markdown":32},"Rumus gerak parabola","info","Komponen kecepatan awal: $v_{0x} = v_0\\cos\\theta$ dan $v_{0y} = v_0\\sin\\theta$.\n\nPosisi setiap saat: $x = v_{0x}\\,t$ dan $y = v_{0y}\\,t - \\tfrac12 g t^2$.\n\n$$t_{\\text{puncak}} = \\frac{v_0\\sin\\theta}{g} \\qquad h_{\\text{maks}} = \\frac{v_0^2\\sin^2\\theta}{2g} \\qquad x_{\\text{maks}} = \\frac{v_0^2\\sin 2\\theta}{g}$$\n\nRumus $x_{\\text{maks}}$ dan waktu terbang $T = 2\\,t_{\\text{puncak}}$ berlaku jika titik awal dan titik akhir sama tinggi.","callout",{"id":35,"data":36,"type":26},"s2-1",{"markdown":37},"## Apa Itu Gerak Parabola?\n\nBola basket yang dilempar ke ring, bola yang ditendang ke gawang, dan air yang memancar dari selang yang dimiringkan bergerak melengkung. Lintasan lengkung itu berbentuk **parabola**, dan bendanya disebut **proyektil**.\n\nSetelah lepas dari tangan, satu-satunya gaya yang dianggap bekerja adalah gaya gravitasi ke bawah. Akibatnya:\n\n- Pada sumbu **x** (mendatar) tidak ada percepatan, sehingga benda bergerak **GLB**.\n- Pada sumbu **y** (tegak) percepatannya $-g$, sehingga benda bergerak **GLBB**: naik makin lambat, lalu turun makin cepat.\n\nKedua gerak ini terjadi bersamaan dan memakai **waktu yang sama**. Itulah kunci menyelesaikan soal gerak parabola.",{"id":39,"data":40,"type":26},"s3-1",{"markdown":41},"## Rumus Kecepatan dan Posisi pada Sumbu x dan y\n\nPilih titik lempar sebagai (0, 0), sumbu x mendatar, dan sumbu y ke atas. Kecepatan awal $v_0$ membentuk sudut elevasi $\\theta$ terhadap tanah, lalu diuraikan menjadi $v_{0x} = v_0\\cos\\theta$ dan $v_{0y} = v_0\\sin\\theta$.\n\nPada setiap saat $t$:\n\n- Kecepatan mendatar tetap: $v_x = v_0\\cos\\theta$.\n- Kecepatan tegak berubah: $v_y = v_0\\sin\\theta - g\\,t$.\n- Posisi: $x = v_0\\cos\\theta \\cdot t$ dan $y = v_0\\sin\\theta \\cdot t - \\tfrac12 g t^2$.\n- Besar kecepatan: $v = \\sqrt{v_x^2 + v_y^2}$.\n\nDi titik puncak, $v_y = 0$, tetapi $v_x$ tetap ada. Jadi, benda tidak berhenti di puncak; benda hanya berhenti naik.",{"id":43,"data":44,"type":26},"s4-1",{"markdown":45},"## Rumus Tinggi Maksimum, Waktu Terbang, dan Jarak Terjauh\n\nDari syarat $v_y = 0$ di puncak, diperoleh waktu ke puncak $t_{\\text{puncak}} = v_0\\sin\\theta \u002F g$. Substitusi ke persamaan $y$ memberi **tinggi maksimum** $h_{\\text{maks}} = v_0^2\\sin^2\\theta \u002F (2g)$.\n\nJika benda mendarat setinggi titik lemparnya, **waktu terbang** $T = 2v_0\\sin\\theta \u002F g$ dan **jarak terjauh** $x_{\\text{maks}} = v_0\\cos\\theta \\cdot T = v_0^2\\sin 2\\theta \u002F g$. Langkah terakhir memakai identitas $2\\sin\\theta\\cos\\theta = \\sin 2\\theta$.\n\nDua fakta penting dari rumus jarak terjauh:\n\n1. Untuk kelajuan awal yang sama, jarak terjauh dicapai pada sudut 45°, karena $\\sin 90^\\circ = 1$.\n2. Dua sudut yang jumlahnya 90°, misalnya 30° dan 60°, menghasilkan jarak terjauh yang sama.\n\nJika titik akhir lebih tinggi atau lebih rendah daripada titik awal, jangan memakai rumus $T$ dan $x_{\\text{maks}}$ di atas. Cari waktunya dari persamaan $y$ dengan ketinggian akhir yang benar.",{"id":47,"data":48,"type":33},"visual-guide",{"title":49,"variant":31,"markdown":50},"Eksplorasi visual","- Atur **Kelajuan awal** 20 m\u002Fs dan **Sudut elevasi** 45°. Cocokkan hasilnya: jarak terjauh sekitar 40,82 m, tinggi maksimum 10,20 m, dan waktu terbang 2,886 s (g = 9,8 m\u002Fs²).\n- Geser **Waktu pengamatan** ke tengah lintasan, sekitar 1,443 s. Di titik puncak ini, posisi mendatarnya sekitar 20,41 m.\n- Ubah sudut menjadi 30°, lalu 60°. Jarak terjauh keduanya sama, sekitar 35,35 m, tetapi tinggi maksimum dan waktu terbangnya berbeda.\n- Kembalikan sudut ke 45° dan ubah kelajuan dari 20 m\u002Fs menjadi 10 m\u002Fs. Jarak terjauh turun menjadi sekitar 10,20 m, seperempatnya, karena sebanding dengan v₀².",{"id":52,"data":53,"type":57},"visual",{"height":54,"assetId":55,"caption":56},520,"demo-v2-asset-projectile","Simulasi gerak parabola","interactive",{"id":59,"data":60,"type":26},"s5-1",{"markdown":61},"## Eksplorasi Visual: Simulasi Gerak Parabola\n\nSimulasi di atas memakai $g = 9{,}8$ m\u002Fs², tanpa hambatan udara, dengan titik awal dan akhir sama tinggi. Ubah kelajuan awal dan sudut elevasi, lalu bandingkan angka pada simulasi dengan hasil hitunganmu. Setelan awalnya 20 m\u002Fs dan 45°, sama dengan Contoh 1 di bawah.",{"id":63,"data":64,"type":26},"s6-1",{"markdown":65},"## Contoh Soal Gerak Parabola dan Pembahasan\n\n### Contoh 1: sudut 45°\n\nBola ditendang dengan kelajuan 20 m\u002Fs pada sudut elevasi 45°. Tentukan waktu terbang, tinggi maksimum, dan jarak terjauh.\n\nPembahasan: $v_{0x} = v_{0y} = 20\\cos 45^\\circ \\approx 14{,}142$ m\u002Fs.\n\n- Waktu terbang: $T = 2(14{,}142) \u002F 9{,}8 \\approx 2{,}886$ s.\n- Tinggi maksimum: $h_{\\text{maks}} = (14{,}142)^2 \u002F (2 \\times 9{,}8) = 200 \u002F 19{,}6 \\approx 10{,}20$ m.\n- Jarak terjauh: $x_{\\text{maks}} = 20^2 \\sin 90^\\circ \u002F 9{,}8 = 400 \u002F 9{,}8 \\approx 40{,}82$ m.\n\nCek: $v_{0x} \\times T = 14{,}142 \\times 2{,}886 \\approx 40{,}81$ m. Selisih kecil berasal dari pembulatan.\n\n### Contoh 2: sudut 30° dan 60°\n\nKelajuan awal tetap 20 m\u002Fs. Bandingkan hasil untuk sudut 30° dan 60°.\n\nPembahasan untuk 30°: $v_{0y} = 20\\sin 30^\\circ = 10$ m\u002Fs, sehingga $T = 20 \u002F 9{,}8 \\approx 2{,}041$ s, $h_{\\text{maks}} = 100 \u002F 19{,}6 \\approx 5{,}10$ m, dan $x_{\\text{maks}} = 400\\sin 60^\\circ \u002F 9{,}8 \\approx 35{,}35$ m.\n\nUntuk 60°: $v_{0y} = 20\\sin 60^\\circ \\approx 17{,}321$ m\u002Fs, sehingga $T \\approx 3{,}535$ s dan $h_{\\text{maks}} = 300 \u002F 19{,}6 \\approx 15{,}31$ m. Jarak terjauhnya juga sekitar 35,35 m karena $\\sin 120^\\circ = \\sin 60^\\circ$.\n\n### Contoh 3: posisi bola pada waktu tertentu\n\nPada Contoh 1, di mana posisi bola setelah 1 s?\n\nPembahasan: $x = 14{,}142 \\times 1 \\approx 14{,}14$ m dan $y = 14{,}142(1) - \\tfrac12(9{,}8)(1^2) = 14{,}142 - 4{,}9 \\approx 9{,}24$ m. Bola masih naik karena 1 s lebih kecil daripada $t_{\\text{puncak}} \\approx 1{,}443$ s.",{"id":67,"data":68,"type":26},"s7-1",{"markdown":69},"## Kesalahan yang Sering Terjadi",{"id":71,"data":72,"type":33},"s7-2",{"title":73,"variant":74,"markdown":75},"Perhatikan sebelum menghitung","warning","- Menganggap kecepatan di puncak nol. Yang nol hanya komponen tegak $v_y$.\n- Menganggap gravitasi hilang di puncak. Percepatan $-g$ bekerja sepanjang lintasan.\n- Kalkulator dalam mode radian padahal sudut ditulis dalam derajat.\n- Memakai rumus jarak terjauh untuk benda yang dilempar dari atas gedung atau mendarat di tempat yang lebih tinggi.",{"id":77,"data":78,"type":33},"s7-3",{"title":79,"variant":80,"markdown":81},"Nilai g dalam soal","tip","Banyak soal memakai $g = 10$ m\u002Fs² agar hitungan lebih mudah. Materi dan simulasi ini memakai $g = 9{,}8$ m\u002Fs². Selalu gunakan nilai g yang disebutkan soal.",{"id":83,"data":84,"type":26},"s8-1",{"markdown":85},"## Ringkasan\n\n- Gerak parabola = GLB mendatar + GLBB tegak, dengan waktu yang sama.\n- $v_{0x} = v_0\\cos\\theta$ dan $v_{0y} = v_0\\sin\\theta$; di puncak hanya $v_y$ yang nol.\n- $h_{\\text{maks}} = v_0^2\\sin^2\\theta\u002F(2g)$ dan $x_{\\text{maks}} = v_0^2\\sin 2\\theta\u002Fg$ untuk titik awal dan akhir sama tinggi.\n- Jarak terjauh maksimum pada 45°; sudut yang jumlahnya 90° memberi jarak yang sama.",{"id":87,"data":88,"type":26},"s9-1",{"markdown":89},"## Materi Terkait\n\n- [GLB dan GLBB](\u002Fmateri\u002Fglb-dan-glbb): dua gerak penyusun gerak parabola.\n- [Hukum Newton 2](\u002Fmateri\u002Fhukum-newton-2): mengapa percepatan proyektil hanya $g$ ke bawah.\n- [Usaha dan Energi](\u002Fmateri\u002Fusaha-dan-energi): cara energi untuk menghitung kelajuan di ketinggian tertentu.\n- Lihat semua materi di [halaman mapel Fisika](\u002Fmapel\u002Ffisika).",{"id":91,"data":92,"type":26},"sources",{"markdown":93},"## Sumber belajar\n\n- [OpenStax Physics — Projectile Motion](https:\u002F\u002Fopenstax.org\u002Fbooks\u002Fphysics\u002Fpages\u002F5-3-projectile-motion)\n\nPenjelasan dan contoh disusun ulang untuk materi ini; sumber dapat dibuka untuk belajar lebih lanjut.",{"id":95,"data":96,"type":99},"practice",{"title":97,"questionSetId":98},"Latihan soal Gerak Parabola","demo-v2-p-fisika-sma-2","quiz",5,1,"2026-10-08T23:58:23.326Z",{"id":20,"slug":104,"name":105,"color":106,"icon":107},"fisika","Fisika","#0EA5E9","atom",[109],{"id":110,"slug":111,"name":112},"cmuzbyhdb000271r9up0bfli4","sma","SMA",[114],{"id":115,"slug":14,"name":116,"subjectId":20},"cmuzbyhfl001e71r9jgkx07y8","Gerak Parabola",[],{"assets":119,"videos":133,"questionSets":134},{"demo-v2-asset-projectile":120},{"id":55,"slug":121,"kind":122,"title":56,"description":123,"url":17,"posterUrl":17,"config":124,"subject":132},"simulasi-gerak-parabola","GRAPH_2D","Ubah kelajuan dan sudut elevasi. Geser waktu untuk membaca posisi, jangkauan, dan tinggi maksimum.",{"a":101,"b":125,"c":125,"xMax":100,"xMin":126,"yMax":100,"yMin":126,"angle":127,"model":128,"omega":129,"slope":101,"speed":130,"gravity":131,"amplitude":101,"intercept":125},0,-5,45,"projectile",2,20,9.8,{"id":20,"slug":104,"name":105},{},{"demo-v2-p-fisika-sma-2":135},{"id":98,"slug":136,"title":137,"mode":138,"description":139,"questionCount":140,"durationMinutes":17},"latihan-soal-gerak-parabola","Latihan Soal Gerak Parabola","PRACTICE","4 soal Gerak Parabola (Fisika SMA) lengkap dengan pembahasan langkah demi langkah dan alasan pilihan yang keliru.",4,[142,168,183,199],{"id":143,"type":144,"slug":145,"title":146,"excerpt":147,"coverUrl":17,"status":18,"publishedAt":148,"featured":5,"readingMinutes":149,"order":125,"updatedAt":150,"subject":151,"levels":152,"topics":166,"tags":167,"author":17},"demo-v2-a-fisika","ARTICLE","belajar-fisika-online","Belajar Fisika Online dari Nol: Materi SD sampai Kuliah","Panduan 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Lanjut.","2026-10-08T09:24:41.485Z",{"id":316,"subjectId":20,"levelId":110,"parentId":17,"slug":1669,"name":1670,"description":1671,"order":1672,"createdAt":1673,"updatedAt":1673},"gelombang-cahaya","Gelombang Cahaya","Gelombang Cahaya — Kelas 11.",17,"2026-10-08T09:24:41.150Z",{"id":400,"subjectId":217,"levelId":110,"parentId":17,"slug":1675,"name":1676,"description":1677,"order":1672,"createdAt":1678,"updatedAt":1678},"transformasi-geometri","Transformasi Geometri","Transformasi Geometri — Kelas 11 Lanjut.","2026-10-08T09:24:41.498Z",{"id":346,"subjectId":217,"levelId":110,"parentId":17,"slug":1680,"name":1681,"description":1682,"order":1683,"createdAt":1684,"updatedAt":1684},"fungsi-dan-pemodelannya","Fungsi dan Pemodelannya","Fungsi dan Pemodelannya — Kelas 11 Lanjut.",18,"2026-10-08T09:24:41.504Z",{"id":382,"subjectId":20,"levelId":110,"parentId":17,"slug":1686,"name":1687,"description":1688,"order":1683,"createdAt":1689,"updatedAt":1689},"optik","Optik","Optik — Kelas 11.","2026-10-08T09:24:41.161Z",{"id":257,"subjectId":217,"levelId":110,"parentId":17,"slug":1691,"name":265,"description":1692,"order":1693,"createdAt":1694,"updatedAt":1694},"barisan-dan-deret-kelas-12-wajib","Barisan dan Deret — Kelas 12 Wajib.",19,"2026-10-08T09:24:41.512Z",{"id":555,"subjectId":20,"levelId":110,"parentId":17,"slug":1696,"name":1697,"description":1698,"order":1693,"createdAt":1699,"updatedAt":1699},"suhu-dan-kalor","Suhu dan Kalor","Suhu dan Kalor — Kelas 11.","2026-10-08T09:24:41.169Z",{"id":286,"subjectId":217,"levelId":110,"parentId":17,"slug":1701,"name":1702,"description":1703,"order":130,"createdAt":1704,"updatedAt":1704},"bunga","Bunga","Bunga — Kelas 12 Wajib.","2026-10-08T09:24:41.518Z",{"id":352,"subjectId":20,"levelId":110,"parentId":17,"slug":1706,"name":1707,"description":1708,"order":130,"createdAt":1709,"updatedAt":1709},"teori-kinetik-gas","Teori Kinetik Gas","Teori Kinetik Gas — Kelas 11.","2026-10-08T09:24:41.188Z",{"id":561,"subjectId":217,"levelId":110,"parentId":17,"slug":1711,"name":1712,"description":1713,"order":1714,"createdAt":1715,"updatedAt":1715},"investasi-dan-pinjaman","Investasi dan Pinjaman","Investasi dan Pinjaman — Kelas 12 Wajib.",21,"2026-10-08T09:24:41.525Z",{"id":579,"subjectId":20,"levelId":110,"parentId":17,"slug":1717,"name":1718,"description":1719,"order":1714,"createdAt":1720,"updatedAt":1720},"termodinamika","Termodinamika","Termodinamika — Kelas 11.","2026-10-08T09:24:41.202Z",{"id":507,"subjectId":217,"levelId":110,"parentId":17,"slug":1722,"name":1723,"description":1724,"order":1725,"createdAt":1726,"updatedAt":1726},"kaidah-pencacahan","Kaidah Pencacahan","Kaidah Pencacahan — Kelas 12 Wajib.",22,"2026-10-08T09:24:41.540Z",{"id":448,"subjectId":20,"levelId":110,"parentId":17,"slug":1728,"name":1729,"description":1730,"order":1725,"createdAt":1731,"updatedAt":1731},"listrik-statis","Listrik Statis","Listrik Statis — Kelas 12.","2026-10-08T09:24:41.215Z",{"id":418,"subjectId":20,"levelId":110,"parentId":17,"slug":1733,"name":1734,"description":1735,"order":1736,"createdAt":1737,"updatedAt":1737},"listrik-arus-searah","Listrik Arus Searah","Listrik Arus Searah — Kelas 12.",23,"2026-10-08T09:24:41.227Z",{"id":466,"subjectId":217,"levelId":110,"parentId":17,"slug":1739,"name":1589,"description":1740,"order":1736,"createdAt":1741,"updatedAt":1741},"peluang-kelas-12-wajib","Peluang — Kelas 12 Wajib.","2026-10-08T09:24:41.547Z",{"id":430,"subjectId":217,"levelId":110,"parentId":17,"slug":1743,"name":1744,"description":1745,"order":1746,"createdAt":1747,"updatedAt":1747},"geometri-analitik","Geometri Analitik","Geometri Analitik — Kelas 12 Lanjut.",24,"2026-10-08T09:24:41.553Z",{"id":424,"subjectId":20,"levelId":110,"parentId":17,"slug":1749,"name":1750,"description":1751,"order":1746,"createdAt":1752,"updatedAt":1752},"kemagnetan","Kemagnetan","Kemagnetan — Kelas 12.","2026-10-08T09:24:41.245Z",{"id":298,"subjectId":217,"levelId":110,"parentId":17,"slug":1754,"name":1755,"description":1756,"order":1757,"createdAt":1758,"updatedAt":1758},"limit","Limit","Limit — Kelas 12 Lanjut.",25,"2026-10-08T09:24:41.562Z",{"id":250,"subjectId":20,"levelId":110,"parentId":17,"slug":1760,"name":1761,"description":1762,"order":1757,"createdAt":1763,"updatedAt":1763},"listrik-ac-arus-bolak-balik","Listrik AC \u002F Arus Bolak Balik","Listrik AC \u002F Arus Bolak Balik — Kelas 12.","2026-10-08T09:24:41.263Z",{"id":489,"subjectId":20,"levelId":110,"parentId":17,"slug":1765,"name":1766,"description":1767,"order":1768,"createdAt":1769,"updatedAt":1769},"gelombang-elektromagnetik","Gelombang Elektromagnetik","Gelombang Elektromagnetik — Kelas 12.",26,"2026-10-08T09:24:41.273Z",{"id":304,"subjectId":217,"levelId":110,"parentId":17,"slug":1771,"name":1772,"description":1773,"order":1768,"createdAt":1774,"updatedAt":1774},"turunan-fungsi","Turunan Fungsi","Turunan Fungsi — Kelas 12 Lanjut.","2026-10-08T09:24:41.575Z",{"id":513,"subjectId":217,"levelId":110,"parentId":17,"slug":1776,"name":1777,"description":1778,"order":1779,"createdAt":1780,"updatedAt":1780},"aplikasi-turunan","Aplikasi Turunan","Aplikasi Turunan — Kelas 12 Lanjut.",27,"2026-10-08T09:24:41.587Z",{"id":543,"subjectId":20,"levelId":110,"parentId":17,"slug":1782,"name":1783,"description":1784,"order":1779,"createdAt":1785,"updatedAt":1785},"pengantar-instrumental-digital","Pengantar Instrumental Digital","Pengantar Instrumental Digital — Kelas 12.","2026-10-08T09:24:41.283Z",{"id":388,"subjectId":217,"levelId":110,"parentId":17,"slug":1787,"name":1788,"description":1789,"order":1790,"createdAt":1791,"updatedAt":1791},"integral","Integral","Integral — Kelas 12 Lanjut.",28,"2026-10-08T09:24:41.599Z",{"id":531,"subjectId":20,"levelId":110,"parentId":17,"slug":1793,"name":1794,"description":1795,"order":1790,"createdAt":1796,"updatedAt":1796},"relativitas-khusus","Relativitas Khusus","Relativitas Khusus — Kelas 12.","2026-10-08T09:24:41.291Z",{"id":537,"subjectId":20,"levelId":110,"parentId":17,"slug":1798,"name":1799,"description":1800,"order":1801,"createdAt":1802,"updatedAt":1802},"gejala-kuantum","Gejala Kuantum","Gejala Kuantum — Kelas 12.",29,"2026-10-08T09:24:41.303Z",{"id":436,"subjectId":217,"levelId":110,"parentId":17,"slug":1804,"name":1805,"description":1806,"order":1801,"createdAt":1807,"updatedAt":1807},"penerapan-integral","Penerapan Integral","Penerapan Integral — Kelas 12 Lanjut.","2026-10-08T09:24:41.607Z",{"id":328,"subjectId":217,"levelId":110,"parentId":17,"slug":1809,"name":1810,"description":1811,"order":1812,"createdAt":1813,"updatedAt":1813},"analisis-data-peluang","Analisis Data & Peluang","Analisis Data & Peluang — Kelas 12 Lanjut.",30,"2026-10-08T09:24:41.611Z",{"id":472,"subjectId":20,"levelId":110,"parentId":17,"slug":1815,"name":1816,"description":1817,"order":1812,"createdAt":1818,"updatedAt":1818},"fisika-inti-dan-radioaktivitas","Fisika Inti dan Radioaktivitas","Fisika Inti dan Radioaktivitas — Kelas 12.","2026-10-08T09:24:41.318Z",{"id":1820,"subjectId":217,"levelId":110,"parentId":17,"slug":1821,"name":1822,"description":1823,"order":1824,"createdAt":1825,"updatedAt":1825},"cmuzbyhw700gw71r9o87lq7vd","logaritma","Logaritma","Logaritma — Kelas 12 Lanjut.",31,"2026-10-08T09:24:41.623Z",{"id":1827,"subjectId":217,"levelId":110,"parentId":17,"slug":1828,"name":1829,"description":1830,"order":1831,"createdAt":1832,"updatedAt":1832},"cmuzbyhw900gy71r9d9sjh9ie","program-linier","Program Linier","Program Linier — Kelas 12 Lanjut.",32,"2026-10-08T09:24:41.625Z",{"id":1834,"subjectId":217,"levelId":110,"parentId":17,"slug":1835,"name":1836,"description":1837,"order":1838,"createdAt":1839,"updatedAt":1839},"cmuzbyhwb00h071r97764r7hr","bangun-ruang","Bangun Ruang","Bangun Ruang — Kelas 12 Lanjut.",33,"2026-10-08T09:24:41.627Z",{"id":1841,"subjectId":217,"levelId":163,"parentId":17,"slug":1842,"name":306,"description":1843,"order":1844,"createdAt":1845,"updatedAt":1845},"demo-v2-topic-matematika-kuliah-1","definisi-turunan-limit","Definisi turunan dengan limit f′(x) = lim [f(x+h) − f(x)]\u002Fh, langkah menghitungnya, gradien garis singgung, syarat diferensiabel, dan contoh soal.",100,"2026-10-08T23:58:22.977Z",{"id":1847,"subjectId":217,"levelId":110,"parentId":17,"slug":1848,"name":1849,"description":1850,"order":1844,"createdAt":1851,"updatedAt":1851},"demo-v2-topic-matematika-sma-1","fungsi-kuadrat","Fungsi Kuadrat","Fungsi kuadrat f(x) = ax² + bx + c: pengaruh a, b, c pada grafik, rumus titik puncak, sumbu simetri, diskriminan, dan contoh soal nilai maksimum.","2026-10-08T23:58:22.868Z",{"id":1853,"subjectId":228,"levelId":110,"parentId":17,"slug":1854,"name":1855,"description":1856,"order":1844,"createdAt":1857,"updatedAt":1857},"demo-v2-topic-pemrograman-sma-1","fungsi-python-def-return","Fungsi Python","Pelajari cara membuat fungsi Python dengan def, parameter, nilai default, dan return, plus perbedaan return dan print lewat contoh program yang jelas.","2026-10-08T23:58:23.661Z",{"id":1859,"subjectId":20,"levelId":158,"parentId":17,"slug":1860,"name":1861,"description":1862,"order":1844,"createdAt":1863,"updatedAt":1863},"demo-v2-topic-fisika-smp-1","glb-dan-glbb","GLB dan GLBB","Rumus GLB dan GLBB lengkap: jarak, kecepatan, percepatan, grafik posisi–waktu, perbedaan GLB dan GLBB, plus contoh soal gerak lurus dan pembahasannya.","2026-10-08T23:58:23.189Z",{"id":211,"subjectId":20,"levelId":163,"parentId":17,"slug":201,"name":212,"description":203,"order":1844,"createdAt":1865,"updatedAt":1865},"2026-10-08T23:58:23.364Z",{"id":1867,"subjectId":20,"levelId":110,"parentId":17,"slug":1868,"name":1869,"description":1870,"order":1844,"createdAt":1871,"updatedAt":1871},"demo-v2-topic-fisika-sma-1","hukum-newton-2","Hukum Newton 2","Hukum Newton 2: bunyi, rumus ΣF = m·a, diagram gaya, gaya gesek statis dan kinetis, serta contoh soal mencari percepatan dan massa beserta pembahasan.","2026-10-08T23:58:23.280Z",{"id":1873,"subjectId":228,"levelId":163,"parentId":17,"slug":1874,"name":1875,"description":1876,"order":1844,"createdAt":1877,"updatedAt":1877},"demo-v2-topic-pemrograman-kuliah-1","notasi-big-o-kompleksitas-waktu","Notasi Big O","Pahami notasi Big O dan kompleksitas waktu algoritma: O(1), O(log n), O(n), O(n²), cara menghitungnya dari kode Python, dan contoh soalnya.","2026-10-08T23:58:23.797Z",{"id":1879,"subjectId":228,"levelId":154,"parentId":17,"slug":1880,"name":1881,"description":1882,"order":1844,"createdAt":1883,"updatedAt":1883},"demo-v2-topic-pemrograman-sd-1","pengertian-algoritma","Pengertian Algoritma","Algoritma adalah langkah-langkah urut untuk menyelesaikan masalah. Pelajari pengertian, ciri, dan contoh algoritma sehari-hari untuk siswa SD.","2026-10-08T23:58:23.477Z",{"id":1885,"subjectId":20,"levelId":154,"parentId":17,"slug":1886,"name":1887,"description":1888,"order":1844,"createdAt":1889,"updatedAt":1889},"demo-v2-topic-fisika-sd-1","pengukuran-panjang","Pengukuran Panjang","Belajar pengukuran panjang untuk SD: satuan baku, alat ukur panjang, cara memakai penggaris, dan tangga satuan panjang km sampai mm + contoh soal.","2026-10-08T23:58:23.095Z",{"id":1891,"subjectId":217,"levelId":154,"parentId":17,"slug":1892,"name":1893,"description":1894,"order":1844,"createdAt":1895,"updatedAt":1895},"demo-v2-topic-matematika-sd-1","penjumlahan-pecahan","Penjumlahan Pecahan","Cara penjumlahan pecahan berpenyebut sama dan beda penyebut memakai KPK, pecahan senilai, dan pecahan campuran, lengkap dengan contoh soal SD.","2026-10-08T23:58:22.508Z",{"id":1897,"subjectId":217,"levelId":158,"parentId":17,"slug":1898,"name":1899,"description":1900,"order":1844,"createdAt":1901,"updatedAt":1901},"demo-v2-topic-matematika-smp-1","teorema-pythagoras","Teorema Pythagoras","Teorema Pythagoras a² + b² = c² untuk mencari sisi miring dan sisi siku-siku, tripel Pythagoras, diagonal ruang balok, dan contoh soal kelas 8.","2026-10-08T23:58:22.690Z",{"id":1903,"subjectId":228,"levelId":158,"parentId":17,"slug":1904,"name":1905,"description":1906,"order":1844,"createdAt":1907,"updatedAt":1907},"demo-v2-topic-pemrograman-smp-1","variabel-dan-tipe-data-python","Variabel dan Tipe Data Python","Belajar variabel dan tipe data Python dari nol: int, float, string, boolean, operator, print, dan input, lengkap dengan contoh program dan latihan.","2026-10-08T23:58:23.562Z",{"id":1909,"subjectId":228,"levelId":163,"parentId":17,"slug":1910,"name":1911,"description":1912,"order":1913,"createdAt":1914,"updatedAt":1914},"demo-v2-topic-pemrograman-kuliah-2","class-dan-object-python","Class dan Object Python","Pelajari class dan object Python untuk OOP: __init__, self, atribut, method, inheritance, dan invarian objek lewat contoh program dompet digital.",101,"2026-10-08T23:58:23.830Z",{"id":1916,"subjectId":217,"levelId":110,"parentId":17,"slug":1917,"name":1918,"description":1919,"order":1913,"createdAt":1920,"updatedAt":1920},"demo-v2-topic-matematika-sma-2","eksponen-dan-logaritma","Eksponen dan Logaritma","Materi eksponen dan logaritma kelas 10: sifat-sifat eksponen, definisi dan sifat logaritma, persamaan eksponen dan logaritma, serta contoh soal.","2026-10-08T23:58:22.902Z",{"id":1922,"subjectId":20,"levelId":154,"parentId":17,"slug":1923,"name":1924,"description":1925,"order":1913,"createdAt":1926,"updatedAt":1926},"demo-v2-topic-fisika-sd-2","macam-macam-gaya","Gaya dan Macam-Macamnya","Gaya adalah tarikan atau dorongan. Pelajari macam-macam gaya (otot, gravitasi, magnet, gesek, pegas), pengaruhnya pada benda, dan contoh soalnya.","2026-10-08T23:58:23.126Z",{"id":1928,"subjectId":217,"levelId":154,"parentId":17,"slug":1929,"name":1930,"description":1931,"order":1913,"createdAt":1932,"updatedAt":1932},"demo-v2-topic-matematika-sd-2","rumus-keliling-dan-luas-bangun-datar","Keliling dan Luas Bangun Datar","Rumus keliling dan luas bangun datar: persegi, persegi panjang, segitiga, jajargenjang, trapesium, dan lingkaran, dengan cara mudah dan contoh soal.","2026-10-08T23:58:22.588Z",{"id":1934,"subjectId":228,"levelId":110,"parentId":17,"slug":1935,"name":1936,"description":1937,"order":1913,"createdAt":1938,"updatedAt":1938},"demo-v2-topic-pemrograman-sma-2","list-dan-dictionary-python","List dan Dictionary Python","Pahami list dan dictionary Python: indeks, append, key-value, get, dan perulangan, plus perbedaan keduanya lewat contoh pengolahan data nilai siswa.","2026-10-08T23:58:23.694Z",{"id":1940,"subjectId":20,"levelId":158,"parentId":17,"slug":1941,"name":1942,"description":1943,"order":1913,"createdAt":1944,"updatedAt":1944},"demo-v2-topic-fisika-smp-2","rumus-massa-jenis","Massa Jenis","Rumus massa jenis ρ = m\u002FV lengkap dengan satuan kg\u002Fm³ dan g\u002Fcm³, tabel massa jenis air, besi, dan minyak, cara menghitung, serta contoh soal pembahasan.","2026-10-08T23:58:23.217Z",{"id":1946,"subjectId":228,"levelId":158,"parentId":17,"slug":1947,"name":1948,"description":1949,"order":1913,"createdAt":1950,"updatedAt":1950},"demo-v2-topic-pemrograman-smp-2","percabangan-python-if-else","Percabangan Python","Pelajari percabangan Python dengan if, elif, dan else: operator perbandingan, operator logika, dan contoh program nilai rapor lengkap dengan outputnya.","2026-10-08T23:58:23.592Z",{"id":1952,"subjectId":228,"levelId":154,"parentId":17,"slug":1953,"name":1954,"description":1955,"order":1913,"createdAt":1956,"updatedAt":1956},"demo-v2-topic-pemrograman-sd-2","percabangan-dalam-algoritma","Percabangan dalam Algoritma","Percabangan dalam algoritma memilih tindakan berdasarkan syarat jika-maka. Pelajari pengertian, contoh sehari-hari, dan simbol flowchart-nya.","2026-10-08T23:58:23.503Z",{"id":1958,"subjectId":217,"levelId":158,"parentId":17,"slug":1959,"name":1960,"description":1961,"order":1913,"createdAt":1962,"updatedAt":1962},"demo-v2-topic-matematika-smp-2","persamaan-garis-lurus","Persamaan Garis Lurus","Persamaan garis lurus y = mx + c, rumus gradien dari dua titik, garis sejajar dan tegak lurus, cara menggambar grafik, serta contoh soal kelas 8.","2026-10-08T23:58:22.730Z",{"id":196,"subjectId":20,"levelId":163,"parentId":17,"slug":185,"name":197,"description":187,"order":1913,"createdAt":1964,"updatedAt":1964},"2026-10-08T23:58:23.394Z",{"id":1966,"subjectId":217,"levelId":110,"parentId":17,"slug":1967,"name":1968,"description":1969,"order":1970,"createdAt":1971,"updatedAt":1971},"demo-v2-topic-matematika-sma-3","rumus-peluang","Peluang Kejadian","Rumus peluang P(A) = n(A)\u002Fn(S), ruang sampel, peluang komplemen, frekuensi harapan, kejadian saling lepas dan saling bebas, plus contoh soal dadu dan koin.",102,"2026-10-08T23:58:22.934Z",{"id":1973,"subjectId":228,"levelId":110,"parentId":17,"slug":1974,"name":1975,"description":1976,"order":1970,"createdAt":1977,"updatedAt":1977},"demo-v2-topic-pemrograman-sma-3","pencarian-linear-dan-biner","Pencarian Linear dan Biner","Pelajari pencarian linear dan pencarian biner (binary search): cara kerja, syarat data terurut, kode Python, dan perbandingan jumlah langkahnya.","2026-10-08T23:58:23.724Z",{"id":1979,"subjectId":228,"levelId":158,"parentId":17,"slug":1980,"name":1981,"description":1982,"order":1970,"createdAt":1983,"updatedAt":1983},"demo-v2-topic-pemrograman-smp-3","perulangan-python-for-while","Perulangan Python","Pelajari perulangan Python dengan for, range(), dan while, lengkap dengan contoh program menghitung total, break, continue, dan latihan soal.","2026-10-08T23:58:23.624Z",{"id":1985,"subjectId":228,"levelId":154,"parentId":17,"slug":1986,"name":1987,"description":1988,"order":1970,"createdAt":1989,"updatedAt":1989},"demo-v2-topic-pemrograman-sd-3","perulangan-dalam-algoritma","Perulangan dalam Algoritma","Perulangan dalam algoritma mengulang langkah yang sama beberapa kali. Pelajari pengertian, contoh perulangan sehari-hari, dan cara menghitung hasilnya.","2026-10-08T23:58:23.529Z",{"id":1991,"subjectId":217,"levelId":158,"parentId":17,"slug":1992,"name":1993,"description":1994,"order":1970,"createdAt":1995,"updatedAt":1995},"demo-v2-topic-matematika-smp-3","rumus-prisma-dan-limas","Prisma dan Limas","Rumus volume prisma dan limas, luas permukaan, sifat sisi-rusuk-titik sudut, jaring-jaring, limas 3D interaktif, dan contoh soal bangun ruang sisi datar.","2026-10-08T23:58:22.780Z",{"id":1997,"subjectId":228,"levelId":163,"parentId":17,"slug":1998,"name":1999,"description":2000,"order":1970,"createdAt":2001,"updatedAt":2001},"demo-v2-topic-pemrograman-kuliah-3","unit-test-python","Unit Test Python","Pelajari unit test Python dengan modul unittest: assertEqual, assertRaises, nilai batas, dan cara menjalankan tes, lengkap dengan contoh dan versi pytest.","2026-10-08T23:58:23.864Z",{"id":2003,"subjectId":217,"levelId":163,"parentId":17,"slug":2004,"name":2005,"description":2006,"order":1970,"createdAt":2007,"updatedAt":2007},"demo-v2-topic-matematika-kuliah-3","vektor-3-dimensi-dot-product","Vektor 3D dan Dot Product","Vektor 3 dimensi: komponen, panjang vektor, vektor satuan, dot product atau perkalian titik, sudut antara dua vektor, proyeksi, dan contoh soal.","2026-10-08T23:58:23.045Z",{"id":2009,"subjectId":217,"levelId":154,"parentId":17,"slug":2010,"name":2011,"description":2012,"order":1970,"createdAt":2013,"updatedAt":2013},"demo-v2-topic-matematika-sd-3","rumus-volume-kubus","Volume dan Luas Permukaan Kubus","Rumus volume kubus V = s³ dan luas permukaan kubus L = 6s², sifat kubus, jaring-jaring, kubus 3D interaktif, dan contoh soal bertingkat.","2026-10-08T23:58:22.619Z",{"id":2015,"subjectId":217,"levelId":158,"parentId":17,"slug":2016,"name":2017,"description":2018,"order":2019,"createdAt":2020,"updatedAt":2020},"demo-v2-topic-matematika-smp-4","rumus-tabung-dan-kerucut","Tabung dan Kerucut","Rumus volume tabung dan kerucut, luas permukaan, garis pelukis, jaring-jaring berupa persegi panjang dan juring, kerucut 3D interaktif, dan contoh soal.",103,"2026-10-08T23:58:22.828Z",{"id":2022,"subjectId":228,"levelId":110,"parentId":17,"slug":2023,"name":2024,"description":2025,"order":2019,"createdAt":2026,"updatedAt":2026},"demo-v2-topic-pemrograman-sma-4","try-except-python","Try Except dan Membaca File","Pelajari try except Python untuk menangani error seperti ValueError dan FileNotFoundError, serta cara membaca dan menulis file txt dengan with open.","2026-10-08T23:58:23.755Z",{"id":2028,"subjectId":217,"levelId":154,"parentId":17,"slug":2029,"name":2030,"description":2031,"order":2019,"createdAt":2032,"updatedAt":2032},"demo-v2-topic-matematika-sd-4","rumus-volume-balok","Volume dan Luas Permukaan Balok","Rumus volume balok V = p × l × t dan luas permukaan balok L = 2(pl + pt + lt), sifat balok, jaring-jaring, balok 3D interaktif, dan contoh soal.","2026-10-08T23:58:22.651Z",[]]