I-Calculator yokushaya kwe-Projectile
Ubukhulu, ubude obuphezulu, isikhathi sokuhamba kanye ne-curve yokuhamba egcwele yokuqashwa.
Iziphetho zivuselelwa uma ubhala.
Malunga nale khadi
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.
Imibuzo ebuzwa kaningi
Yini i-angle yokuqashwa enikeza ubukhulu bokulinganisa?
Kumhlaba ofanayo ngaphandle kokulwa kwezulu, 45° unikeza ubukhulu obukhulu ngoba sin(2θ) ufinyelela ku-θ = 45°. Ukuqashwa okuphezulu kushintsha i-optimum ibe phansi.
Ingabe lezi zimali ze-projectile zitholakali?
Ukuhamba ngokuthe nkqo kuhlela isikhathi sokuhamba kusuka ku-v·sinθ ne-gravity; umkhawulo yisikhathi esihambayo esihambayo v·cosθ esiphindaphindwa ngalolu sikhathi. Ubude obuphezulu yi-(v·sinθ)²/(2g).
Kungani 30° ne 60° zinikeza umkhawulo ofanayo?
Kumhlaba ophakeme, umkhawulo uxhomekeke ku sin(2θ), no sin(60°) = sin(120°), ngakho-ke ama-angles ahambisanayo angeza ku 90° akhiqiza umkhawulo ofanayo. U shot 60° uhamba phezulu futhi uhlala uhamba phezulu; u shot 30° ushesha futhi ushesha.
Ingabe lokhu kuchaza ukumelana nezulu?
Hayi - icabanga ukuthi kunesikhala, ngakho-ke ukunyakaza kwelanga kuyisici esinjalo. Ukukhanya okungokoqobo noma izinto ezisheshayo zihamba kancane uma kuqhathaniswa nenani elicalwa ngoba ukudonsa kususa isivinini. Imodeli ilungile kakhulu kuma-projectiles aqinile, ahamba kancane.
Yini ezoba uma ngiqala kusuka ephakeme?
Misela ubude bokuqala ngaphezu kwe-zero futhi i-projectile idinga ukuphakama okude ukuwa, ngakho ihlala phezulu isikhathi eside futhi ihamba eduze, futhi i-angle engcono kakhulu yokuhamba okuphezulu ikhuphuka ama-degrees ambalwa ngaphansi kuka-45°. I-pathway izoba i-parabola engalingani.
Uhlu lwezimoto ezihamba phambili
Ihlanganisa isivinini esihamba phambili (esingaguquki) nesivinini esihamba phambili lapho iwela khona nge-Pythagorean theorem. Ukuqashwa kusuka esiteji sezulu ezindaweni eziqinile, isivinini sokuphazamisa silingana nesikhathi sokuqala ngokulondolozwa kwe-energy; kusuka ephakeme iphakeme.
API — sebenzisa le calculator kusuka kukhodi
Nquma le calculator njenge JSON evulekile yendawo yokuqeda - akukho isithonjana esidingekayo. Thumela amaxabiso endawo ngezansi njengezilungiselelo zombuzo noma i-JSON. Noma yini ongayishiya isebenzisa iphutha elifanayo elifakwe ngaphambili lekhasi; ipharamitha engaziwa yi-400, ayikho i-zero emnyama. Funda i-API egcwele →
Ingxenye yendawo
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);Izibalo ziyisilinganiso esisetshenziswa ukuqondisa kuphela, hhayi ukucebisa ngezimali, ukwelashwa noma ukukhokha.