Kalkulator Gerakan Projectile
Saben pesawat, pesawat, lan pesawat terbang, iku dipérang dadi rong jinis.
Hasil dioptimalake nalika sampeyan ngetik.
Ngendi kalkulator iki
Projectile motion describes anything launched into the air and left to gravity — a thrown ball, a fired shell, a jet of water. The trick is that the horizontal and vertical motions are independent: horizontally the object moves at a constant vx = v·cos(θ), while vertically it decelerates, stops and falls back under gravity g at vy = v·sin(θ) initially. With no air resistance and launching from level ground, the range is v²·sin(2θ)/g, the maximum height is (v·sin θ)²/(2g), and the total flight time follows from the vertical motion. Standard gravity is g = 9.80665 m/s².
As a worked example, launch at 20 m/s and 45° on level ground: vx = vy = 20 × 0.707 ≈ 14.14 m/s, the range is 20²·sin(90°)/9.807 ≈ 40.8 m, the peak height is 14.14²/(2×9.807) ≈ 10.2 m, and it stays airborne about 2.9 s. The calculator returns the range, peak height, flight time, the horizontal and vertical speed components and the impact speed, and plots the full parabolic trajectory.
On level ground the maximum range occurs at a 45° launch, because sin(2θ) peaks there; complementary angles like 30° and 60° give the same range but different heights and flight times. Set a launch height above ground under advanced options — for a projectile fired from a cliff or a thrown ball released at shoulder height — and the optimal angle drops slightly below 45°. These results ignore air resistance, so they overestimate the range of light or fast objects, but they are the standard model for sports, ballistics and physics problems.
Takon kang asring diajukake
Apa kang dadi titik awal lan titik pungkasan?
Ing taun 2009, 45% saka populasi donya wis ngalami gangguan iki, lan 45% saka populasi donya wis ngalami gangguan iki.
Apa kang dadi tujuané?
Gerakan vertikal nyetel wektu lelungan saka v·sinθ lan gravitasi; jarak iku kecepatan horisontal v·cosθ kang dikalikan karo wektu iku. Jarak maksimum ya iku (v·sinθ)²/(2g).
30° lan 60° punika sami-sami dipunginakaken.
Ing tanah kang rata jaraké gumantung marang sin(2θ), lan sin(60°) = sin(120°), mula sudut komplementer kang ditambahaké marang 90° ngasilaké jarak kang padha.
Apa iku kaanan ing atmosfer?
Ora - iki nganggep vakum, mula gravitasi iku siji-sijiné gaya. Cahya nyata utawa obyek kang cepet ora bisa tekan jarak kang dikalkulake amarga drag nyegah kecepatan. Model iki paling akurat kanggo proyektil kang padat, lan bergerak alon.
Apa kang kelakon nalika aku miwiti saka dhuwur?
Sawisé iku, suhu ing permukaan bumi bakal mundhak lan bakal tekan titik paling dhuwur ing 45 derajat, lan banjur bakal mudhun manèh nganti tekan titik paling endhek ing 40 derajat.
Apa kang diarani kecepatan?
Iki nggabungake kecepatan horisontal (ora dipérang-pérang) karo kecepatan vertikal nalika mendarat nganggo teorema Pythagorean. Nalika diluncuraké saka tingkat lemah ing tlatah rata, kecepatan impact padha karo kecepatan peluncuran kanthi konservasi energi; saka dhuwur iku luwih dhuwur.
API — gunakake kalkulator iki saka kode
Panggenan kalkulator iki minangka titik pungkasan JSON gratis - ora ana kunci sing dibutuhaké. Kirimi nilai medan ing ngisor iki minangka parameter pitakonan utawa JSON. Anything you omit uses the same default this page is pre-filled with; an unknown parameter is a 400, never a silent zero. Waca dokumen API lengkap →
Titik pungkasan
GET https://calculator.free/api/v1/projectile-motion/curl
curl "https://calculator.free/api/v1/projectile-motion/?velocity=20&angle=45"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/projectile-motion/?" + new URLSearchParams({
"velocity": "20",
"angle": "45"
}));
const data = await r.json();
console.log(data.results);Kajaba iku, ana uga sing ora bisa gawé gawéan, kaya ta dokter, insinyur, lan liya-liyané.