Kifaa cha Kukadiria Mabadiliko
Safu, kilele, wakati wa kuruka na mpindo kamili wa chombo cha kurushia angani.
Matokeo yanakuwa bora zaidi unapochapa.
Kuhusu kifaa hiki cha kupigia hesabu
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.
Maswali yaliyoulizwa mara nyingi
Ni pembe gani ya kurushwa angani ambayo ndiyo sehemu ya juu zaidi?
On level ground with no air resistance, 45° gives the greatest range because sin(2θ) peaks at θ = 45°. A raised launch shifts the optimum slightly lower.
Kanuni hizo zenye kuvutia hupatikanaje?
Vertical motion sets the flight time from v·sinθ and gravity; the range is the horizontal speed v·cosθ multiplied by that time. Max height is (v·sinθ)²/(2g).
Why do 30° and 60° give the same range?
On level ground the range depends on sin(2θ), and sin(60°) = sin(120°), so complementary angles that add to 90° produce the same distance. The 60° shot goes higher and stays airborne longer; the 30° shot is flatter and faster.
Je, hilo linamaanisha kwamba ndege hao wanaweza kukinza hewa?
Hakuna COPH inayochukua nafasi, kwa hiyo uvutano ndio kani pekee. Nuru halisi au vitu vyepesi hupungukiwa na kiwango kinachokadiriwa kwa sababu damu huvuja kasi.
Ni nini hutukia ninaporushwa kutoka juu?
Set a launch height above zero and the projectile has farther to fall, so it stays up longer and travels farther, and the optimal angle for maximum range drops a few degrees below 45°. The trajectory becomes an asymmetric parabola.
Mwendo wa mgongano hupatikanaje?
Unaunganisha mwendo wa mlalo (bila kubadilishwa kotekote) na mwendo wa kusimama wa kutua kupitia Pythagorean astorem.
API bustanini hutumia kifaa hiki cha hesabu kutoka kwenye mfumo wa sheria
Ipigie simu kifaa hiki cha kupigia hesabu kama Junse É not doot toder. Chochote unachoacha kinatumia kiwango kilekile cha mwisho ambacho ukurasa huu haujakamilika; parameta isiyojulikana ni 400, si sufuri kimya kamwe. Soma habari kamili za API docs →
keyboard label
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);Matokeo ni makadirio ya mwongozo wa ujumla, si wa kifedha, wa kitiba au wa kodi tu.