Projectile Motion Calculator
Wyling, hoogtehoogte, vliegtyd en die volle lugboog van'n boot.
Resultate werk op soos jy tik.
Aangaande hierdie sakrekenaar
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.
Dikwels gevra vrae
Watter lanseerhoek gee die maksimum omvang?
Op gelyk grond sonder lugweerstand gee 45 graad die grootste verspreiding omdat sondeeë van die π2 Abrolhos) by π = 45 grade bereik.'n Opgestelde lanseerrit maak die besteum effens laer.
Hoe word hierdie projektiele waardes gevind?
Vertical motion sets the flight time from v·sinθ and gravity; the range is the horizontal speed v·cosθ multiplied by that time. Max height is (v·sinθ)²/(2g).
Waarom gee 30 graad en 60 graad dieselfde?
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.
Is dit die rede vir lugweerstand?
Geen ium dit neem 'n vakuum aan nie, so swaartekrag is die enigste krag. Ware lig of vinnige voorwerpe skiet te kort aan die berekende omvang omdat trek bloei van spoed. Die model is uiters akkuraat vir digte, stadige projektilasies.
Wat gebeur wanneer ek van'n hoogte af begin stap?
Stel 'n begin hoogte bo nul en die projektiele het verder om te val, so dit bly langer en reis verder, en die optimale hoek vir maksimum omvang daal 'n paar grade onder 45 grade. Die tikkie word 'n asimmetrie parabola.
Hoe word die impakspoed gevind?
Dit kombineer die horisontale spoed (wat regdeur) met die vertikale spoed om via die Pythagorean - torem te land.'n Verandering van grondvlak op plat terrein is die impakspoed gelyk aan die lanseerspoed deur energiebewaring; van'n hoogte is dit hoër.
API ← gebruik hierdie sakrekenaar van kode
Bel hierdie sakrekenaar as 'n vry JSON-punt takies wat nodig is. Stuur die veldwaardes hieronder as navraag parameters of JSON. Enigiets wat jy weglaat gebruik dieselfde verstek hierdie bladsy is vooraf gevul met; 'n onbekende parameter is 'n 400, nooit' n stil nul. Lees die volle API docs →
Einde punt:
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);Die resultate is skattings van algemene leiding, nie net finansiële, mediese of belastingvoorligting nie.