Projectile Motion Calculator
Range, peak height, flight nguva uye yakazara trajectory curve yekutanga.
Zvinyorwa zvinogadziridzwa paunenge uchinyora.
Nezve iyi kalkulator
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.
Zvimwe zvinobvunzwa zvakanyanya
Chii kuvhura angle inopa mazhinji marudzi?
Panzvimbo yakaenzana pasina kumanikidza kwemhepo, 45° inokupa iwe mukana mukuru wekuita izvi nekuti sin(2θ) inosvika pa θ = 45°. A raised launch shifts the optimum slightly lower.
Maitiro ekuwana izvi zviyero zvemufananidzo?
Kufamba kwe vertical kunopa nguva yendege kubva ku v·sinθ ne gravity; iyo nzvimbo ndeyekukwira kwe horizontal v·cosθ kwakapetwa nenguva. Max height is (v·sinθ)²/(2g).
Nei 30° ne60° zvichipa imwe chete nzvimbo?
Panzvimbo yakaenzana, kukwira kunoenderana ne sin(2θ), uye sin(60°) = sin(120°), saka maangles anowedzera kune 90° anopa kukwira kwechinzvimbo chimwe chete. 60° shot inokwira uye inoramba ichifamba kwenguva yakareba; 30° shot inoita kunge yakapfava uye inofamba nekukurumidza.
Chii chinoita kuti mhepo irambe ichibata?
Hapana — inofunga kuti pane vacuum, saka gravity ndiyo chete simba. Real light kana zvinhu zvinofamba zvakaoma kusvika pakufungidzirwa kwenzvimbo nekuti kumanikidza kunobvisa simba. Iyo model inonyanya kunyatsojeka kune yakaoma, inofamba-famba zvidimbu.
Chii chinoitika kana ini ndichitanga kubva panzvimbo yakakwira?
Kana ukaisa kukwira kwechiedza pamusoro pezero, chiedza chinoramba chiri pedyo nenzvimbo yacho, saka chinoramba chiri pedyo nenzvimbo yacho, uye iyo angle yakakwana yekumhanya kunogona kukwira kusvika kumadhigirii mashoma pasi pe45°.
Sei kuitika kwesimba kunogona kuwanikwa?
Inosanganisira kutenderera kwemhepo (kubva pasi kusvika pamusoro) pamwe nekutenderera kwemhepo (kubva pamusoro kusvika pasi) kuburikidza nePythagorean theorem. Kutanga kubva panzvimbo yepasi, kutenderera kwemhepo kunoenzaniswa nekufamba kwemhepo nesimba rekuchengeta simba. Kutanga kubva panzvimbo yepasi, kutenderera kwemhepo kunoenzaniswa nekufamba kwemhepo nesimba rekuchengeta simba.
API — kushandisa iyi kalkulator kubva code
Nhare iyi calculator semahara JSON endpoint - hapana chikuru zvinodiwa. Kutumira nzvimbo mavara pasi separameter query kana JSON. Chii zvachose chaunoisa kunze chinoshandisa default iyo peji iri rakasviba nayo; parameter isiri yechokwadi inonzi 400, uye haisi zero. Tora yakazara API docs →
Endpoint
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);Zviratidzo zvemubvunzo ndezvekufungidzira kwechinangwa chekudzidzisa chete, kwete zvemari, zvehutano kana zvemari.