I-Projectile Motion Calculator
Uluhlu, ubude obuphezulu, ixesha lokuhamba kunye nobubanzi bokuhamba kwenqwelo-moya.
Iinketho ze projekti
Malunga nale Calculator
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 ebuza rhoqo
I-engile yokuqalisa inika ubukhulu bokufikelela?
Kwindawo ethe tyaba engenakumelana nomoya, i-45° inika umgama omkhulu kuba i-sin(2θ) iphakama kwi-θ = 45°. Ukuqalisa okuphezulu kutshintshela okulungileyo okuncinci ezantsi.
Zifunyanwa njani ezi xabiso zeprotheyini?
Intshukumo ethe nkqo imisela ixesha lokuhamba ukusuka kwi v·sinθ kunye nobunzima bezinto; umgama ukhawuleziso oluthe tyaba v·cosθ oluphindwe kabini ngaloo xesha. Ubude obuphezulu buyi (v·sinθ)²/(2g).
Kutheni i-30° ne-60° inika umgama ofanayo?
Kwindawo ethe tyaba umgama uxhomekeke kwisin (2θ), kunye nesin (60°) = sin (120°), ngoko ke i-engile ehambelanayo edibanisa kwi-90° ivelisa umgama ofanayo. Uhlaselo lwe-60° luya phezulu luhlala luhamba ngenqwelo-moya ixesha elide; uhlaselo lwe-30° luhle kwaye lukhawulezayo.
Ingaba le nkqubo ichaza ukumelana komoya?
Hayi - icinga ukuba akukho nto ijikelezayo, ngoko uxinzelelo lunamandla olunye. Izinto ezikhanyayo okanye ezikhawulezayo zithatha ixesha elide ukufikelela kwinqanaba elicalulweyo kuba ukutsala kukhupha umsinga. Imodeli ichanekile kakhulu kwizinto eziqinileyo, ezihamba ngamandla amancinci.
Yintoni eyenza ukuba ndiqale ukusuka phezulu?
Misela ubude bokuqala ngaphezulu kwesiqingatha kwaye i-proyector ifuna ukuwela phezulu, ngoko ihlala phezulu ixesha elide kwaye ihamba phezulu, kwaye i-engile efanelekileyo yokufikelela okuphezulu ikhupha amaqondo ambalwa ngaphantsi kwe-45°. Ukuhamba kwendlela kwenziwa ibe yiparabola engalinganiyo.
Ukhawulezo lokubetha lufunyenwe njani?
Idibanisa uxinzelelo oluthe tyaba (alungenziwanga tshintsho) noxinzelelo oluthe nkqo xa iwela nge-Pythagoras theorem. Ukuqalisa ukusuka kwinqanaba lehlabathi kwindawo ethambileyo, uxinzelelo loxinzelelo lulingana noxinzelelo lokuqalisa ngokugcina amandla; ukusuka kwinqanaba liphezulu.
API — sebenzisa le calculator ukusuka kwikhowudi
Nceda le khadi lemali njengendawo esemva ye-JSON ekhululekileyo - akukho qhosha lifunekayo. Thumela amaxabiso endawo ezantsi njengeparameter yombuzo okanye i-JSON. Nantoni na oyenzayo isebenzisa okungagqibekanga okufanayo eli phepha ligqityiwe ngaphambili; iparameter engaziwayo yi 400, ayikho i zero ekhululekileyo. Funda i-API epheleleyo →
Incopho yesiphelo
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);Results are estimates for general guidance only, not financial, medical or tax advice.