Proýekt hereket hasapçy
A launch's range, peak height, flight time and full trajectory curve.
Netijeler ýazýan wagtyň täzelener.
Bu hasapçy hakda
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.
Köp soralýan soraglar
Näme başlatma çuňlugy iň köp aralygy berýär?
Eýwanyň garşylyksyz düz ýere, 45° iň uly aralygy berýär sebäbi sin(2θ) 45°-da çägini alýar. Bir galdyrylan başlatma optimaly biraz aşakda üýşýär.
Bu proýekt mykdarlary nädip tapylýar?
Dikey hereket v·sinθ we gravitasiýadan uçuş wagtyny belleýär; aralyk horizontal tizlik v·cosθ bilen bu wagt bilen çarpylan. Maks. beýiklik (v·sinθ)²/(2g)
Näme üçin 30° we 60° deň aralyk berýär?
On level ground the range depends on sin(2θ), and sin(60°) = sin(120°), so complementary angles that add to 90° produce the same distance. The 60° shot goes higher and stays airborne longer; the 30° shot is flatter and faster.
Bu howa garşylyklymy?
Haýal däl - ol boşluky kabul edýär, şonuň üçin gravitasiýa diňe güýçdür. Akyly ýagty ýa-da tiz nesneler hasaplanan aralykdan azrakdyr sebäbi çekiş hızıny azaltýar. Model iň dogry çuň, yavaş hereket eden proýektiler üçindir.
Men bir beýiklikden başlasam näme bolar?
Sıfryň üstünden bir başlatmak beýikligini goý we proýektiniň düşmek üçin uzakrak ýoly bar, şoňa görä ol uzakrak saklanýar we uzakrak ýola çykýar, we iň uly aralyk üçin iň gowy burç 45° aşakda birnäçe derejä düşýär. Traýekt asimmetrik parabola öwrülýär.
Eňmek tizligi nädip tapylýar?
Bu Pitagoras teoremasy arkaly düşmekde dikey tizlik bilen horizontal tizlik (bütinleý üýtgemeýän) birleşdirir. Yer derejesinden düz ýere uçmakda, tizlik energiýa saklamak arkaly düşmek tizligine deňdir; beýiklikden bolsa has ýokary.
API — bu hasapçyny koddan ullan
Bu hasapçyny boş JSON ahtar noktasy hökmünde çagyr - açar gerek däl. Aşakdaky meýdança mykdarlaryny soragyň parametrleri ýa-da JSON hökmünde iber. Siziň goýmaýan hernäňiz şu sahypanyň öň bellenen öň bellenenini ulanýar; namydar parametr 400, hiç wagt sessiz sıfır däl. Eňlisçe senedleri oka →
Endpoint
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);Netijeler diňe umumy ýardam üçin hasaplanypdyr, maliýe, saglyk ýa-da salgyt maslahaty üçin däl.