Računalo gibanja projektila
Razpon, najvišja višina, čas leta in polna krivulja poti izstrelitve.
Rezultati posodabljajo, ko tipkate.
O tem kalkulatorju
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.
Pogosta vprašanja
Kateri izstrelni kot daje največji doseg?
On level ground with no air resistance, 45° gives the greatest range because sin(2θ) peaks at θ = 45°. A raised launch shifts the optimum slightly lower.
Kako so te pogonske vrednosti najdene?
Navpično gibanje nastavi čas leta od v·sinλ in težnosti; razpon je vodoravna hitrost v·cosı pomnožena s tem časom. Najvišja višina je (v·sinλ)2/(2g).
Zakaj 30° in 60° dajeta enak obseg?
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.
Ali to pomeni odpor zraku?
Ne – to predvideva vakuum, tako da je gravitacija edina sila. Pravi svetloba ali hitro objekti padejo iz izračunanega razpona, ker vleče krvavitev iz hitrosti. Model je najbolj natančen za goste, počasi premikanje projektil.
Kaj se zgodi, ko izstrelim iz višine?
Nastavite izstrelitev višino nad ničlo in projektil je daljši, tako da ostane dlje in potuje daljše, in optimalni kot za največji doseg pada nekaj stopinj pod 45°. Pot postaneš asimetrična parabola.
Kako se ugotovi hitrost udarca?
Združuje vodoravno hitrost (nespremenjena skozi) z navpično hitrostjo pri pristanku preko Pitagorske teoreme. Od začetka tal na ravni tečaj, udarna hitrost je enaka hitrosti izstrelitve z ohranjanjem energije; od višine je višja.
API – uporabi ta kalkulator iz kode
Poišči ta kalkulator kot brezplačni končni cilj JSON – ni potreben ključ. Pošljite spodnje vrednosti polja kot parametre za poizvedovanje ali JSON. Vse, kar opustite, uporablja enako privzeto. Ta stran je napolnjena z; neznani parameter je 400, nikoli ne tiho ničlo. Preberite celoten API docs →
Končna točka
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);Rezultati so ocene za splošne smernice, ne pa za finančne, zdravniške ali davčne nasvete.