Projectile Motion Calculator
Kajaba ti éta, jarak, kecepatan, lan jarak tempuh pesawat ogé diitung.
Hasilne bakal dioptimalake nalika sampeyan ngetik.
Ngenai 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-takon kang kerep diajukake
Apa sudut peluncuran sing menehi jarak maksimal?
Dina kaayaan normal, suhuna 45 °C. Dina kaayaan anu paling parah, suhuna bisa nepi ka 50 °C. Dina kaayaan anu paling parah, suhuna bisa nepi ka 100 °C.
Kepiye carane nilai-nilai projectile iki ditemokake?
Gerakan vertikal ngawatesan waktos terbang ti v·sinθ jeung gravitasi; jangkungna nyaéta laju horisontal v·cosθ dikalikan ku waktos éta. Jangkungna maksimum nyaéta (v·sinθ)²/(2g).
30° lan 60° iku jarak sing padha.
Dina permukaan rata jarakna gumantung kana sin(2θ), sarta sin(60°) = sin(120°), jadi sudut komplementer anu ditambahkeun ka 90° ngahasilkeun jarak anu sami. Shot 60° ngaleuwihan sarta tetep dina udara langkung lami; shot 30° langkung rata sarta gancang.
Apa iki tegese resistensi udara?
Teu — éta ngaduga vakum, jadi gravitasi nyaéta hiji-hijina kakuatan. Objek anu semu atanapi gancang henteu cocog sareng jarak anu dikalkulasikeun sabab drag ngaleungitkeun laju. Modelna paling akurat pikeun proyektil anu padat, gerak lambat.
Apa sing kedadeyan nalika aku miwiti saka dhuwur?
Nyatetkeun jangkungna pelepasan di luhur nol, sarta proyéktil bakal leuwih jauh ti leungeun, jadi éta bakal tetep di luhur leuwih lila sarta bakal leumpang leuwih jauh, sarta sudut optimal pikeun jarak maksimum bakal turun sababaraha derajat handapeun 45°. Trayektori jadi parabola asimétris.
Carane kecepatan impact ditemokake?
Ieu ngagabungkeun laju horisontal (teu dirobah) jeung laju vertikal nalika naek ku teorema Pythagorean. Ngaleupaskeun ti tingkat tanah dina lahan rata, laju tumbukan sarua jeung laju leupaskeun ku konservasi energi; ti luhurna lajuna leuwih luhur.
API — gunakake kalkulator iki saka kode
Ngadongékeun kalkulator ieu minangka titik akhir JSON bébas — teu peryogi kunci. Kirim nilai medan di handapeun minangka parameter pitakonan atawa 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 lengkap API →
Tampilan
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);Hasilna nyaéta perkiraan pikeun pituduh umum, henteu saran finansial, médis atanapi pajak.