Kalkulator pokreta projektila
Domet, vrhunac visine, vrijeme leta i puna krivulja putanje lansiranja.
Rezultati ažuriranja dok kucate.
O ovom kalkulatoru
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.
Česta pitanja
Koji kut lansiranja daje maksimalni domet?
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 se pronađu te vrijednosti projektila?
Okomiti pokret postavlja vrijeme leta od v·sinλ i gravitacije; raspon je vodoravna brzina v·cosλ pomnožena za to vrijeme. Maksimalna visina je (v·sinλ)2/(2g).
Zašto 30° i 60° daju isti raspon?
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.
Da li to objašnjava otpor zraka?
Ne — pretpostavlja vakuum, tako da je gravitacija jedina sila. Pravi svjetlo ili brzi objekti ne djeluju u proračunu jer vuče krvarenje off brzine. Model je najtočniji za guste, sporo pomjeranje projektila.
Što će se dogoditi kad lansiram s visine?
Postavite lansirnu visinu iznad nule i projektil ima dalje padati, tako da ostaje duže i putuje dalje, a optimalni kut za maksimalni domet pada nekoliko stupnjeva ispod 45°. Putanja postaje asimetrična parabola.
Kako se nalaze brzine udara?
Ona kombinira horizontalnu brzinu (nepromijenjena kroz) s vertikalnom brzinom pri slijetanju preko Pitagorea teoreme. Pokretanje iz tla na ravnom terenu, udar brzina jednaka brzini lansiranja kroz očuvanje energije; od visine je veća.
API – koristi ovaj kalkulator iz koda
Nazovi ovaj kalkulator kao slobodan JSON ishod — nije potreban ključ. Pošaljite vrijednosti polja ispod kao parametre upita ili JSON. Sve što opustite koristi istu uobičajenu stranicu je napunjena; nepoznati parametar je 400, nikada tiha nula. Pročitajte cijeli API dokumenata →
Krajnji točki
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 su procjene za opće smjernice samo za financijske, medicinske ili porezne savjete.