Áireamhán Tairiscintí
Raon, buaic-ard, am eitilte agus cuar iomlán traicé seolta.
Torthaí a nuashonrú mar a chlóscríobh tú.
Maidir leis an áireamhán seo
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.
Ceisteanna Coitianta
Cén uillinn seolta a thugann an raon uasta?
Ar thalamh cothrom gan aon fhriotaíocht aeir, tugann 45° an raon is mó toisc go mbíonn sin(2θ) ag buaic ag θ = 45°.
Conas a fhaightear na luachanna projectile seo?
Socraíonn gluaiseacht ingearach an t-am eitilte ó v·sinθ agus domhantarraingt; is é an raon an luas cothrománach v·cosθ iolraithe faoin am sin. Is é an airde uasta (v·sinθ)²/(2g).
Cén fáth a dtugann 30° agus 60° an raon céanna?
Ar thalamh cothrom, braitheann an raon ar sin(2θ), agus sin(60°) = sin(120°), mar sin uillinneacha comhlántacha a chur le 90° a tháirgeadh an fad céanna.An lámhaigh 60 ° téann níos airde agus fanann aerbhealaigh níos faide; an lámhaigh 30 ° tá níos réidh agus níos tapúla.
An gcuireann sé seo friotaíocht aeir san áireamh?
Níl — glacann sé le folús, mar sin is é an imtharraingt an t-aon fhórsa amháin. Ní shroicheann réada fíor-solasacha nó réada gasta an raon ríomhtha toisc go n-éireoidh an luas as an tarraingt. Is é an tsamhail is cruinne do diúracáin dhlútha, a ghluaiseann go mall.
Cad a tharlaíonn nuair a sheol mé ó airde?
Socraigh airde seolta os cionn nialas agus tá an diúracáin níos faide le titim, mar sin fanann sé suas níos faide agus taisteal níos faide, agus titeann an uillinn is fearr le haghaidh raon uasta cúpla céim faoi bhun 45 °.
Conas a aimsítear an luas tionchair?
Is é an luas tionchair an luas a bhíonn ag an mbád ag dul i dtreo an talamh. Is é an luas tionchair an luas a bhíonn ag an mbád ag dul i dtreo an talamh. Is é an luas tionchair an luas a bhíonn ag an mbád ag dul i dtreo an talamh.
API — úsáid an áireamhán seo ó chód
Glaoigh ar an áireamhán seo mar chríochphointe JSON saor in aisce - níl aon eochair ag teastáil. Seol na luachanna réimse thíos mar pharaiméadair cheist nó JSON. Anything you omit uses the same default this page is pre-filled with; an unknown parameter is a 400, never a silent zero. Léigh an doiciméadú iomlán API →
Deireadhphointe
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);Is meastacháin iad na torthaí le haghaidh treoir ghinearálta amháin, ní comhairle airgeadais, leighis nó cánach.