Nhazi
Oge ahụ, elu nke pēèk̀òtù, oge ụgbọelu nakwa tráìlụ̀ zuru ezu nke mmepe.
Nhọrọ ndị ahụ ga-akpụzi mgbe ị na-etipụta.
N'ihe banyere calculator a
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.
Ajụjụ ndị a na-ajụkarị
Gịnị bụ malite angụlụ na-enye ọfụụ n'ebe ahụ?
N'elu ala dị n'elu ebe ahụ na-enweghị nrụgide ikuku, 45° na-enye oke n'ihi na sin(2θ) na-abịa n'elu na θ = 45°. Nhazi a na-ebuli elu na-atụgharị n'ihe dị mma n'okpuru.
Olee otú a ga-esi hụ uru ndị a?
Ntụgharị vetikal na-ehazi oge ụgbọelu site na v·sinθ na nrụgide; ọ̀sọ̀ bụ n'ógónụ́ọ̀nụ́ ọsọ v·cosθ a na-ébàtà ya site na oge ahụ. Ogo nke nta bụ (v·sinθ)²/(2g).
Gịnị mere 30° na 60° ji nye n'otu n'otu?
N'elu ala dị n'elu ala, ọ̀sọ̀ na-adabere na sin(2θ), na sin(60°) = sin(120°), ya mere, aịkọn ndị na-agbakwunyere na 90° na-eme ka ọ̀sọ̀ dị ka nke ahụ. 60° shot na-aga elu ma na-adị n'elu elu ogologo oge; 30° shot bụ nke dị n'elu ala ma na-adị ngwa.
Ọ bụ nke a maka nrụgide ikuku?
Ọ dịghị - ọ na-atụ anya vaịkọn, yabụ na ọ bụ nrụgide ka ọ bụ ike ikpeazụ. Nnukwu ọkụ ma ọ bụ ihenhọrọ ndị dị n'okporo ụzọ na-apụta n'ime n'ime n'ihi na ịkpụga na-apụta n'okporo ụzọ. Móòdù ahụ bụ nke kasị n'ókè maka n'ótù, n'ótù-n'ótù-n'ótù.
Gịnị ga-eme ma m malite site n'elu?
Hazie elu nke mmepe n'elu séèfọ̀ ná ọ̀dọ̀ na-ébèghị̀ anya n'ime, ya mere ọ̀ ga-adị elu n'oge ogologo nakwa na-aga n'ebè anya, nakwa aịkọn nke kacha mma maka ogo nke kacha nta na-àdọ̀ n'okpuru 45°. Òtù ahụ na-aghọ asị́mịrá parálọ́ọ̀.
Olee otú okporo ụzọ ahụ na-ahụ?
Ọ na-ejikọta horizon ọsọ (enweghị mgbanwe n'ime) na vatịkal ọsọ na nkwụsị site na Pythagorean theorem. N'ịmalite site n'elu ala na ala dị n'ime, ọsọ nke mmebi ahụ dị otua na ọsọ nke mmebi site n'ịchekwa ike; site n'elu ọ dị elu.
API — jiri kaadị a site na kóòdù
Kpọọ kalkulata a dịka ebe ngwụcha JSON n'efu - enweghị kii achọrọ. Ziga valiu ebe ahụ n'okpuru dịka paramita ajụjụ mọọbụ JSON. Ihe ọbụla ị na-ewepụ na-eji dìfọ́ọ̀ltụ̀ nke a na-edebe ihuakwụkwọ a na ya; parameter a na-amaghị bụ 400, ọ dịghị sẽọ̀rọ̀. Gụọ ngwe ndị ahụ niile →
Ebemkpofuozi
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);Ihe a na-ahụta bụ n'ihi nlekọta n'ozuzu ya, ọ bụghị nlekọta ego, ọgwụ ma ọ bụ nlekọta ego.