Kalkulatè mouvman pwojèk
Li gen yon gwo vitès, yon gwo vitès, yon gwo vitès, yon gwo vitès, yon gwo vitès.
Rezilta yo mete ajou pandan w ap ekri.
Atik sa a
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.
Kesyon ki poze souvan
Ki ang lansman ki bay maksimòm distans la?
Sou tè a plat san okenn rezistans lè, 45 ° bay pi gwo distans paske sin (2θ) pi gwo nan θ = 45 °.
Ki jan yo jwenn valè sa yo?
Mouvman vètikal la defini tan vòl la soti nan v·sinθ ak gravite; distans la se vitès orizontal v·cosθ multiplié pa tan sa a. Altè maksimòm se (v·sinθ)²/(2g).
Poukisa 30° ak 60° bay menm kantite vòt?
Nan tè a plat, distans la depann de sin(2θ), ak sin(60°) = sin(120°), se konsa ang komplementè ki ajoute a 90° pwodwi menm distans la. 60° shot la ale pi wo ak rete nan lè a pi lontan; 30° shot la se pi plat ak pi vit.
Ki sa ki se yon rezistans nan lè?
Pa — li pran pou yon vag, se konsa gravite se fòs la sèlman. Objektif reyèl limyè oswa vit yo pa rive nan lajè calculé paske drag bleeds off vitesse. Modèl la se pi egzat pou pwojèil dense, ki deplase lente.
Ki sa ki rive lè mwen lanse soti nan yon wotè?
Si nou mete yon wotè lansman ki pi wo pase zewo, pwojèyl la gen plis distans pou l tonbe, se sa ki fè li rete pi lontan epi li vwayaje pi lwen, ak ang ki pi bon pou maksimòm distans la tonbe kèk degre anba 45°.
Ki jan vitès impact a te jwenn?
Li konbine vitès orizontal (pa chanje tout wout la) ak vitès vètik nan ateri via teorema Pythagorean. Lanse soti nan nivo tè a sou yon teren plat, vitès la nan enpak egal a vitès lansman an pa konsèvasyon enèji; soti nan yon wotè li se pi wo.
API — itilize sa a calculateur soti nan kòd
Apèl sa a calculateur kòm yon gratis JSON pwent-de-fini - pa gen okenn kle ki nesesè. Envoye valè jaden anba a kòm paramèt kesyonè oswa JSON. Anything you omit uses the same default this page is pre-filled with; an unknown parameter is a 400, never a silent zero. Li dokiman API a an antye →
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);Rezilta yo se estimasyon pou kòmandman jeneral sèlman, pa finansye, medikal oswa konsèy taks.