BAB I
PENDAHULUAN
Bicara tentang fungsi vektor, ada baiknya jika kita tahu terlebih dahulu apa itu vektor. Dalam fisika kita mengenal vektor sebagai sebuah besaran yang memiliki nilai dan arah. Sedangkan dalam matematika, vektor adalah anggota dari ruang vektor. Secara geometris, vektor dapat disajikan dengan ruas garis berarah. Panjang ruas garis menyatakan besar vektor dan anak panah menyatakan arah vektor.
Pada dasarnya, setiap bagian dari matematika memiliki fungsi masing-masing. Baik fungsi matematisnya, penerapannya dalam kehidupan maupun kaitannya dengan ilmu agama. Tidak terkecuali dengan vektor. Secara matematis, kita kadang-kadang menyatakan bahwa sebuah fungsi vektor A (x,y,z) mendefinisikan suatu medan vektor karena mengaitkan suatu vektor dengan setiap titik di suatu daerah. Sementara dari segi kehidupan manusianya, vektor berfungsi misalnya dalam hal teknologi GPS. Sedangkan dari segi agamis, vektor dapat memperlihatkan betapa mulianya Allah SWT. yang telah menciptakan alam semesta beserta manusia dengan sempurnanya.
oleh karena itu kami akan membahas sedikit tentang aplikasi vektor dalam kehidupan sehari-hari.
I.2 Rumusan Masalah
Melalui latar belakang di atas, maka adapun yang menjadi rumusan masalah dalam karya ilmiah ini adalah:
- Apa yang dimaksud dengan vektor itu?
- Apa saja Fungsi vektor?
- Apa saja contoh penerapan vektor dalam kehidupan sehari-hari?
I.3 Tujuan dan Manfaat Penulisan
Berdasarkan rumusan masalah diatas, tujuan dari penulisan karya ilmiah ini adalah:
- Mengetahui apa yang dimaksud dengan vektor.
- Mengetahui Fungsi Vektor.
- Mengetahui Contoh vektor dalam kehidupan sehari-hari.
I.4 Sistematika Penulisan
Karya ilmiah ini terdiri atas 3 Bab. Bab pertama yaitu pendahuluan, berisi latar belakang, rumusan masalah, tujuan penulisan, manfaat penuisan dan sistematika penulisan. Bab kedua berisi pembahasan, dimana pada bab ini, kami menjelaskan apa-apa saja terkait dalam rumusan masalah yang telah dirancang sebelumnya. Dan pada bab terakhir, kami menjelaskan perihal kesimpulan dari seluruh pembahasan disertai dengan saran. Sebagai pertanggung jawaban, kami juga menyertakan Daftar pustaka pada bagian akhir karya ilmiah ini.
BAB II
PEMBAHASAN
Vektor adalah besaran yang mempunyai nilai dan arah. Contoh sebuah kapal bergerak dengan kecepatan sebesar 20 knot pada arah 30 derajat dari suatu pelabuhan. Dari pernyataan di atas dapat dipahami bahwa kapal tersebut bergerak dengan kecepatan 20 knot yang merupakan besaran, selain itu dijelaskan juga arah yang ditempuh, yaitu 30 derajat dari pelabuhan.
Penggambaran vektor:
Untuk menyatakan suatu vektor dapat dilakukan pada bidang datar atau bidang koordinat Cartesius XOY dengan menggambar ruas garis dengan anak panah di salah satu ujungnya. Panjang ruas garis mewakili besar (panjang) vektor dan anak panah mewakili arah vektor. Vektor disimbolkan dengan huruf tebal atau dengan huruf yang digaris bawahi.
Macam-macam vektor:
- Vektor Satuan : Vektor yang memiliki arah, meskipun hanya bernilai satu.
- Vektor Nol : Vektor yang titik awal dan akhirnya sama.
- Vektor Negatif : Negatif sebagai penunjuk arahnya.
- Vektor Posisi : Vektor yang menempati posisi pada bidang kartesius.
- Vektor Ortogonal: Vektor basis pada dimensi tiga.
- Vektor Basis : Vektor yang menempati suatu kartesius.
- Vektor Resultan : Vektor yang menjadi hasil dari semua vektor.
II.2 Fungsi Vektor Secara garis besar
Dalam dunia manusia ini, memang tidak serta merta kita dapat mlihat fungsi dari vektor tersebut. Namun, fungsi itu ada dan itulah sebabnya mata pelajaran/mata kuliah ini tetap dipelajari. Fungsi-fungsi tersebut antara lain yaitu:
1. Sarana transportasi darat, laut, maupun udara masing-masing memiliki peluang yang sama untuk terjadinya kecelakaan. Apabila kecelakaan teradi di tengah lautan lepas tentunya kapal yang mengalami kerusakan hars dibawa ke pelabuhan terdekat untuk segera diperbaiki. Untuk menarik kapal tersebut dibutuhkan dua buah kapal dengan dilengkapi kawat baja. Agar kapal dapat sampai ke pelabuhan yan dituju dan posisi kapal selama perjalanan tetap stabil besar gaya yang dibutuhkan oleh masing-masing kapal penarik dan sudut yang di bentuk oleh kawat baja harus diperhitungkan dengan cermat.
2. Dalam Navigasi, vektor berpengaruh besar terhadap keberadaan suatu lokasi ditinjau dari tempat yang bergerak (kendaraan atau lainnya). Teknologi ini disebut Global Positioning System atau GPS. Dimana sistem ini memberitahukan lokasi di permukaan bumi walaupun tempatnya bergerak. Sehingga, suatu kendaraan dapat tahu keberadaannya dan dimana lokasi tujuannya. Karena itu vektor sangat berperan penting dalam Navigasi contohnya vector yang digunakan untuk Sistem Navigasi Pesawat Terbang. Semua pesawat terbang dilengkapi dengan sistem navigasi agar pesawat tidak tersesat dalam melakukan penerbangan. Panel-panel instrument navigasi pada kokpit pesawat memberikan berbagai informasi untuk sistem navigasi mulai dari informasi tentang arah dan ketinggian pesawat. Pengecekan terhadap instrument sistem navigasi harus seteliti dan seketat mungkin. Sebagai contoh kejadian yang menimpa pesawat Adam Air pada bulan pebruari 2006 sewaktu menjalani penerbangan dari bandara Soekarno Hatta menuju bandara Hasanudin di Makasar. Ketidaktelitian pihak otoritas penerbangan yang mengijinkan pesawat Adam Air terbang dengan sistem navigasi yang tidak berfungsi menyebabkan Pesawat Adam Air berputar-putar di udara tanpa tahu arah selama tiga jam, sebelum mendarat darurat di bandara El Tari Nusa Tenggara Timur. Kesalahan akibat tidak berfungsinya system navigasi adalah kesalahan yang fatal dalam dunia penerbangan. Sanksi yang diberikan adalah dicabutnya ijin operasi bagi maskapai penerbangan yang melanggar. Vektor menyatakan arah dan besar suatu besaran. Jurusan tiga angka, Analisi ruang, Navigasi penerbangan dan pelayaran selalu menggunakan vektor untuk keperluan itu. Peralatan navigasi membutuhkan perhitungan vektoris yang sudah dikalibrasikan dengan alat ukur sehingga menghasilkan keluaran manual atau digital. Keluaran itu dapat dibaca pada pada alat ukur yang menera besar dan arah secara bersamaan, sehingga bermanfaat bagi orang yang memantaunya.
Pernahkah Kamu naik pesawat terbang? Antara penumpang dan pilot dan copilot di ruang kemudi dipisah dengan sekat. Tujuannya agar pilot dapat berkonsentrasi mengemudikan pesawat. Pernahkah Kamu bayangkan pesawat terbang di malam hari? Bagaimana pilot mengemudikan pesawat terbang di malam hari. Dengan sistem vektor yang dikalibrasikan dengan komputer navigasi pesawat pilot dapat memantau arah tujuan pendaratan pesawat. Jadi tidak pernah sebuah pesawat nyasar ke lain tempat.
II.3 Contoh-contoh Vektor dalam kehidupan sehari-hari
Berikut ini adalah beberapa contoh vektor dalam kehidupan sehari-hari yang mungkin tidak asing lagi bagi kita semua.
- Ketika Upacara bendera dihari senin, pasukan paskibra mengibarkan bendera dari bawah ke atas. Aplikasi vektor bendera seperti sudut 90 derajat.
- Ketika seorang melakukan olahraga tersebut, mereka akan terjun dengan kemiringan tertentu hingga menginjak tanah.
- Ketika penerjun menjatuhkan diri dari kapal, tempat ia jatuh tidak tepat di bawah kapal, tetapi jauh melenceng karena adanya dua vektor gaya yaitu gaya gravitasi dan gaya dorong angin.
- Dalam sains komputer vektor digunakan untuk pembuatan gravis. Grafis adalah gambar yang tersusun dari koordinat-koordinat. Dengan demikian sumber gambar yang muncul pada layar monitor komputer terdiri atas titik-titik yang mempunyai nilai koordinat. Layar Monitor berfungsi sebgai sumbu koordinat x dan y. Grafis vektor adalah objek gambar yang dibentuk melalui kombinasi titik-titik dan garis dengan menggunakan rumusan matematika tertentu. Contoh software yang menggunakan vektor adalah CorelDRAW dan Adobe Illustrator. Dalam software komputer seperti AutoCAD, Google SketchUp dll, terdapat penghitungan vektor yang terkomputerisasi. Program tersebut berfungsi sebagai penggambar rancangan bangunan 3D sebelum membangun bangunan sebenarnya. Dalam progeam tersebut terdapat tiga sumbu, sumbu X, sumbu Y dan sumbu Tegak (3 dimensional).
- Kapal selam: kapal. Selam ini di beri rongga udara yang berfungsi sebai tempat masuk dan kluarnya air atau udara. Ketika rongga tersebut berisi udara ,volume air di yang pindahkan sama dengan berat kaPal sehingga kapal selam bisa mengapung.dan jika tutup udara Pada rongga di buka kembali maka volume air pada rongga akan bertambah sehingga kapal selam tenggelam.
BAB III
PENUTUP
Vektor adalah besaran yang mempunyai nilai dan arah. Untuk menyatakan suatu vektor dapat dilakukan pada bidang datar atau bidang koordinat Cartesius XOY dengan menggambar ruas garis dengan anak panah di salah satu ujungnya. Panjang ruas garis mewakili besar (panjang) vektor dan anak panah mewakili arah vektor. Vektor disimbolkan dengan huruf tebal atau dengan huruf yang digaris bawahi.
Kehidupan ini bukan hanya sekedar makan dan minum saja, kita sebagai manusia dituntut untuk mempelajari apa yang telah tuhan berikan kepada kita sebagai manusia makhluk yang paling sempurna, sehingga kita dapat mengetahui kebesaranya.
III.2 Saran
Pembahasan tentang fungsi vektor ini bukan pembahasan singkat yang akan selesai dalam sekali duduk. Masih ada banyak lagi yang belum dibicarakan disini. Untuk itu, diharapkan kita mau mencari sumber-sumber lain diluar sana untuk menambah pengetahuan kita tentang Fungsi vektor dalam segala aspeknya yang belum terjelaskan dalam karya ilmiah ini.
Daftar Pustaka
1. R.Spiegel,Murray.1991.AnalisisVektor.Jakarta: Erlangga
2.http://metricmatik.blogspot.com/2011/04/makalah-kegunaan-kalkulus-vektor.html (24-06-2013/02:53)
3. http://simplemomentum.blogspot.com/2012/05/penerapan-vektor-dalam-kehidupan-sehari.html (24-06-2013/01:34)
Bagus sekali blog saudara, nilai 90. Akan mendapat 100. Jika karya tulis ada sedikit sketza gambar atau foto lukiskan aplikasi vektor dlm kehidupan sehari-hari
BalasHapusterima kasih bapak :)
BalasHapusKomentar ini telah dihapus oleh pengarang.
BalasHapusmakasih :)good job guys (y)
BalasHapusmakasihbuat contoh vektor dalam kehidupan sehari-harinya ^-^.semoga sukses selalu..
BalasHapuswow bagus sekali laporannya... sangat membantu....
BalasHapusmakasih sudah berbagi ilmu
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