Kalkaaliyihii Dhaqdhaqaaqa
Range, dhererka sare, waqtiga duulimaadyada iyo wareegga trajectory buuxa ee la soo bandhigay.
Natiijooyinka cusbooneysiinta sida aad ku qorto.
Ku saabsan Kalkaaliyahan
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.
Su'aalaha badanaa la isweydiiyo
Waa maxay jiididda jiididda siinaysaa xadka ugu badan?
On dhulka heerka leh aan la iska caabin hawada, 45 ° siiyaa heerka ugu weyn sababtoo ah sin (2θ) ku dhaco θ = 45 °. A soo bandhigay kor u dhaqaaqa ugu fiican oo yar hoos.
Sidee ayaa qiimahaan projectile la helay?
Dhaqdhaqaaqa xagalku wuxuu go'aamiya waqtigii duulimaadyada ka soo baxa v·sinθ iyo xoogga dhulka; waajibaadka waa xawaaraha xagal v·cosθ oo la isku daray waqtigaas. Dhererka ugu sarreeya waa (v·sinθ)² / (2g).
Maxaa 30 ° iyo 60 ° siiyaan kala duwanaansho isku mid ah?
On dhulka heerka waajibaadka ku xiran yahay sin (2θ), iyo sin (60 °) = sin (120 °), sidaas daraaddeed geesaha ku xiran oo ku daray 90 ° soo saaraan fogaan isku mid ah. The 60 ° toogasho ka sii sarreeyaa oo sii joogaa hawada dheer; the 30 ° toogasho waa flatter iyo ka dhaqso badan.
Maxaa ka dhigaya in ay tahay in la iska cafiyo hawada?
Ma aha — waxay u maleynayaan in ay tahay meel aan waxba ku jirin, sidaas darteed xoogga culus waa xoogga kaliya. iftiinka dhabta ah ama waxyaabo dhaqso ah oo ka yar xadka la xisaabiyey sababtoo ah dhaqdhaqaaqa ayaa ka baxa xawaaraha.
Maxaa dhacaya marka aan ka bilaabay sare?
Si aad u hesho dhererka soo dejinta sare ee zero iyo projectile waa ka fog in ay hoos u dhacaan, sidaas darteed waa in ay sii joogaan oo ka sii dheer iyo safarka ka sii fog, iyo geeska ugu fiican ee ugu badnaan waa in ay hoos u dhacaan qaar ka mid ah darajo hoos 45 °.
Sidee ayaa xawaaraha saamaynta la helay?
Waxay isku daraan xawaaraha xagal (aan la beddelin oo dhan) la xawaaraha xagal ah ee duulimaadyada ka gudbay Pythagorean theorem. Launching ka dhulka heerka dhulka ku dhul siman, xawaaraha saamaynta waa la mid ah xawaaraha soo dejinta by kaydinta tamarta; ka sare waa ka sarreeya.
API — isticmaal xisaabinta ka code
Wici xisaabinta sida free JSON endpoint - key ma loo baahan yahay. Dib u soo dir qiimaha goobta hoos ku qoran sida parameters su'aal ama JSON. Wax kasta oo aad ka maqan tahay isticmaalaa default la mid ah ee boggani waa hore loo buuxiyey la; parameter aan la aqoon waa 400, marnaba ma aha zero maqan. Akhri dhammaan API xuquuqda →
Xarafka
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);Natiijooyinka waa tirakoobka loogu talagalay tilmaamaha guud oo keliya, maaha dhaqaale, caafimaad ama talo bixin canshuur.