Projectile Motion Calculator
Mlingo, kulemera kwa mapiko, nthawi yonyamula ndege ndi kuzungulira kwa trajectory ya kukhazikitsidwa.
Zithunzizi zimasintha monga momwe mumalemba.
Zachidule
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.
Mafunso ofunsidwa nthawi zambiri
Kodi kukhazikitsa angular amapereka malingana ndi maximum?
Pamalo opanda mpweya wotsutsana, 45° imapatsa kutalika kwakukulu chifukwa sin(2θ) imafika pa θ = 45°. Kuyambira koyamba kumasintha bwino kwambiri pang'onopang'ono.
Kodi ndi mmene izi projectile mfundo anapeza?
Mphatso yozungulira imaika nthawi yoyenda kuchokera ku v·sinθ ndi kupweteka kwa dziko lapansi; mtunda ndi liwiro lozungulira v·cosθ lowonjezeredwa ndi nthawiyo. Kutalika kokwanira ndi (v·sinθ)²/(2g).
N’chifukwa chiyani 30° ndi 60° zimapatsa kutalika kofanana?
Pamalo oyera, mtunda umadalira sin (2θ), ndi sin (60 °) = sin (120 °), kotero ma angles owonjezera omwe amawonjezera 90 ° amapanga mtunda wofanana. 60 ° shot imakhala yotsika kwambiri ndipo imakhala nthawi yayitali; 30 ° shot ndi yolimba kwambiri komanso yofulumira.
Kodi izi zikutanthauza kukana kwa mpweya?
Sichoncho — imaganiza kuti pali vakuumu, choncho gravity ndi mphamvu yokhayo. Maonekedwe abwino kapena zinthu zoyenda mofulumira zimatsika pansi pa mtunda wokalembedwa chifukwa kukana kumakhala kotsika. Model ndi yoyenera kwambiri kwa ma projectiles olimba, oyenda mofulumira.
Kodi chimachitika pamene ine kukhazikitsa kuchokera pa kutalika?
Kukhazikitsa kukhazikitsidwa kwa pamwamba pa zero ndi projectile ali mbali yaitali kuti apite, kotero kuti ali pamwamba m'nthawi yayitali ndi kuyenda mbali yaitali, ndi yabwino angle kwa maximum range amalowetsa mapiri angapo pansi 45 °. The trajectory amayamba kukhala asimetriya parabola.
Kodi ndi chiyani chida chofunikira kwambiri?
It combines the horizontal speed (unchanged throughout) with the vertical speed at landing via the Pythagorean theorem. Launching from ground level on flat terrain, the impact speed equals the launch speed by energy conservation; from a height it is higher.
API — kugwiritsa ntchito izi calculator kuchokera code
Kuti mudziwe zambiri, pitani ku www.json.org/json.html. Kuti mudziwe zambiri, pitani ku www.json.org/json.html. Chomweko chilichonse chimene mumasiya chimagwiritsa ntchito mfundo yoyamba yomweyi yomwe tsambali limagwiritsa ntchito; mfundo yosadziwika ndi 400, siyiyenera kukhala zero yosadziwika. Onani zonse API docs →
Chithunzi
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);Zimenezi ndi zowerengera zokhudzana ndi malangizo amtundu uliwonse, si zokhudzana ndi ndalama, zamoyo kapena zokhudzana ndi ndalama.