projectile-kuyenda

Nkhani yokhudza kuyenda kwa Projectile ndi mavuto a zitsanzo ndi mayankho

Liwiro loyambirira (v)_o) ndi gawo la liwiro loyambirira (v_ox ndi v_oy)

Chinthu chomwe mayendedwe ake a parabolic nthawi zonse amakhala ndi liwiro loyambirira. Chifukwa mayendedwe a parabolic ndi kuphatikiza mayendedwe m'njira zopingasa ndi zoyimirira, liwiro loyambirira limakhalanso ndi zigawo zopingasa ndi zoyimirira.

Ngati chinthucho chikuyenda modabwitsa monga momwe zilili mu Zithunzi 1 ndi 3, ndiye kuti liwiro loyambirira mbali yopingasa (v _ox ) ndi liwiro loyambirira mbali yopingasa (v _oy ) zimawerengedwa pogwiritsa ntchito equation:

v _ox = vo _o cos θ

v _oy = vo _o sin θ

Ngati chinthucho chikuyenda mophiphiritsa monga chithunzi 2 ndiye kuti v _o = v _ox (v _oy = 0)

Liwiro (v)_x ndi v_y) ndi Malo (x ndi y)

Liwiro m'njira zopingasa ndi zoyima pa nthawi inayake limawerengedwa pogwiritsa ntchito equation:

v _x = v _ox = nthawi zonse ( kuyenda kofanana kwa mzere )

v _y = v _oy + gt kapena v _y ² = v _oy ² + 2 gh (kuyenda kopanda kugwa)

Malo a zinthu m'njira yopingasa (x) ndi yoyimirira (y) pa nthawi inayake amawerengedwa pogwiritsa ntchito equation:

x = v _ox t

y = v _oy t + 1⁄2 gt ²

Zotsatira za liwiro (v) ndi malo (h)

Liwiro lotsatira pa nthawi inayake limawerengedwa pogwiritsa ntchito equation:

Kuwongolera kwa zinthu panthawi inayake kumawerengedwa pogwiritsa ntchito equation:

Ndemanga:

1. Gawo lopingasa la kayendedwe ka parabolic limaonedwa ngati kayendedwe kofanana kolunjika, kotero vox = vx nthawi zonse imakhala yokhazikika

2. Gawo loyima la kayendedwe ka parabolic limaonedwa ngati kayendedwe ka free-fall, kotero ngati chinthucho chikuyenda parabolic, monga Zithunzi 1 ndi 3, gawo loyima la liwiro la chinthucho pa kutalika kwakukulu ndi zero (v _y = 0). Ngati muponya marble molunjika mmwamba pa kutalika kwakukulu, chinthucho chimapumula kwakanthawi (v _y = 0) musanatembenukire pansi. Chifukwa chake, liwiro la chinthucho kusuntha parabolic pa kutalika kwakukulu = v _x = v _ox

3. Ngati chinthucho chikuyenda mophiphiritsa monga momwe zasonyezedwera pa Chithunzi 2, gawo loyima la kuyenda mophiphiritsa limawonedwa ngati kuyenda kopanda kugwa. Ngati chinthucho chikuyenda mophiphiritsa monga Zithunzi 1 ndi 3 ndiye kuti gawo loyima la kuyenda mophiphiritsa limawonedwa ngati kuyenda koyima mmwamba).

Mavuto a zitsanzo:

1. Chipolopolo chimawomberedwa mopingasa ndi liwiro loyambirira la 20 m/s. Ngati mfutiyo ili pamtunda wa mamita 5 kuchokera pansi, dziwani izi:

(a) nthawi mumlengalenga

(b) kutalika kwakukulu

(c) mtunda wopingasa

(d) liwiro la chipolopolo chikagunda pansi

yankho;

Kuyenda molunjika kolunjika kumasanthulidwa ngati kuyenda kolunjika kofanana, pomwe kuyenda molunjika kumasanthulidwa ngati kuyenda kopanda kugwa.

Zodziwika:

v _ox = 20 m/s, v _oy = 0 m/s, h = 5 m, g = 9.8 m/s ²

a) Nthawi mumlengalenga

Yankho lake ndi lofanana ndi kudziwa nthawi (t) mu kayendedwe ka free fall.

Kudziwika: v _oy = 0 m/s, h = 5 m, g = 9.8 m/s ²

Ankafuna: t

b) Kutalika kwakukulu

Kutalika kwakukulu = h = mamita 5.

c) Mtunda wopingasa (d)

Yankho lake lili ngati kudziwa mtunda pa kayendedwe kofanana ka mzere

Yodziwika: v _ox = 20 m/s, t = 1 sekondi

Ankafuna: d

d = vt

d = (20 m/s)(1 s) = 20 m

d) Liwiro chipolopolo chikagunda pansi

v _tx = v _ng'ombe = 20 m/s

v _ty = ?

Choyamba, timawerengera liwiro lomaliza molunjika (vty). Yankho lake lili ngati kudziwa liwiro lomaliza la kayendedwe ka free-fall.

Yodziwika: v _oy = 0, g = 9.8 m/s ² , t = 1 s

Akufuna: v _ty

v _t = vo _o + gt —> vo = 0

v _t = gt

v _t = (9.8 m/s ² )(1 s)

v _t = 9.8 m/s

Liwiro la chipolopolo chikagunda pansi:

Njira ya chipolopolo:

Chifukwa v _tx ili moyang'anizana ndi x-axis yabwino (kumanja) ndipo v _ty ili moyang'anizana ndi y-axis yoyipa (pansi),

Njira ya chipolopolocho ikagunda pansi ndi -26.1 ^o kupita ku x-axis yabwino (onani chithunzi pansipa).

2. Mfuti inaponya chipolopolo pa liwiro la 30 ^o kupita mopingasa ndi liwiro la 60 m/s. Dziwani izi:

(a) kutalika kwakukulu

(b) liwiro la chipolopolo pamtunda wapamwamba kwambiri

(c) nthawi mumlengalenga

(d) mtunda wopingasa

(e) liwiro la chipolopolo chikagunda pansi. Tiyerekeze kuti pansi pali thyathyathya. 🙂

yankho;

Kuyenda molunjika kolunjika kumasanthulidwa ngati kuyenda kolunjika kofanana, kuyenda molunjika kumasanthulidwa ngati kuyenda kolunjika kokwera.

Yodziwika: v _o = 60 m/s, theta = 30 ^o.

Kutengera deta yodziwika, choyamba timawerengera zigawo zoyima (v _oy ) ndi zopingasa (v _ox ) za liwiro loyambirira (v _o ).

a) Kutalika kwakukulu (h)

Yankho lake lili ngati kudziwa kutalika kwakukulu pakuyenda molunjika mmwamba.

Zodziwika:

v _ng'ombe = v _o cos θ = (60) (cos 30) = (60) (0.87) = 52 m/s

v _oy = v _o tchimo θ = (60) (tchimo 30) = (60) (0.5) = 30 m/s

a) Kutalika kwakukulu (h)

Yankho lake lili ngati kudziwa kutalika kwakukulu pakuyenda molunjika mmwamba.

Zodziwika:

v _oy = 30 m/s (ili ndi liwiro loyamba la chipolopolo)

v _ty = 0 m/s (Pa kutalika kwakukulu, liwiro loyima la chipolopolo = 0 m/s. Ili ndiye liwiro lomaliza.)

g = – 9.8 m/s ²

Ankafuna: h

v _t ² = v _o ² + 2 gh

0 ² = 30 ² + 2 (-9.8) h

0 = 900 – 19.6 maola

900 = maola 19.6

h = 900 / 19.6

h = mamita 45.9

Kutalika kwakukulu komwe chipolopolocho chinapeza ndi mamita 45.9.

b) Liwiro pa kutalika kwakukulu

Pa kutalika kwakukulu, liwiro lomwe lili kumbali yowongoka = 0 m/s. Pa kutalika kwakukulu, pali liwiro lokhalo lomwe lili kumbali yowongoka. Liwiro lomwe lili kumbali yowongoka pa kutalika kwakukulu ndi lofanana ndi liwiro loyambirira lomwe lili kumbali yowongoka, lomwe ndi 52.2 m/s. Liwiro lomwe lili kumbali yowongoka nthawi zonse limakhala losasintha, ndiko kuti, kumbali ya x-axis yabwino (ngati kuyenda kwa chinthu kwafotokozedwa pachithunzi pamwambapa)

c) Nthawi mumlengalenga

Yankho lake lili ngati kudziwa nthawi (t) pokambirana za kayendedwe kokwera mmwamba koyimirira.

Zodziwika:

v _oy = 30 m/s (ili ndi liwiro loyamba la chipolopolo kumbali yoyima)

g = – 9.8 m/s ²

h = 0 m (chipolopolo chikabwerera pansi, kusuntha kwa chipolopolo mbali yowongoka = 0 m)

Ankafuna: t

h = vot ₊ ½ gt ²

0 = (30) t + ½ (-9.8 m/s ² ) t ²

0 = (30) t – 4.9 t ²

(30) t = 4.9 t ²

30 = 4.9 t

t = 30 / 4.9

t = masekondi awiri

Nthawi mumlengalenga = masekondi 6.12

d) Mtunda wopingasa (d)

Yankho lake lili ngati kudziwa mtunda (d) pa kayendedwe kofanana ka mzere.

Zodziwika:

v _ng'ombe = 52.2 m/s

t = masekondi awiri

Ankafuna: d

d = vt = (52.2 m/s)(masekondi 6.12) = 319.5 m

e) Liwiro chipolopolo chikagunda pansi

v _tx = v _ng'ombe = 52.2 m/s

v _ty = ?

Choyamba, timawerengera liwiro lomaliza molunjika (v _ty ). Yankho lake ndikupeza liwiro lomaliza poyenda molunjika mmwamba.

Akufuna: v _oy = 30 m/s, g = -9.8 m/s ² , t = 6.12 masekondi

Akufuna: v _ty

v _ty = v _oy + gt

v _ty = (30) + (-9.8)(6.12)

v _ty = (30) – (60)

v _ty = -30 m/s

Chizindikiro chosonyeza kuti liwiro lomaliza likutsika. Dziwani kuti liwiro loyambirira lomwe lili kumbali yowongoka ndi lofanana ndi liwiro lomaliza lomwe lili kumbali yowongoka.

Liwiro la chipolopolo chikagunda pansi:

Kulunjika kwa chipolopolo:

Popeza v _tx ili moyang'anizana ndi x-axis yabwino (kumanja) ndipo vty ili moyang'anizana ndi y-axis yoyipa (pansi),

Kuwongolera kwa liwiro la chipolopolocho chikafika pansi ndi -30 ^o pafupifupi x-axis yabwino (onani chithunzi pansipa).

3. Mpira umaponyedwa kuchokera m'mphepete mwa nyumba ya mamita 50 kutalika ndi liwiro loyamba la 10 m/s. Ngati mpirawo waponyedwa pa 30o pafupifupi mopingasa, dziwani izi:

(a) nthawi yomwe mpira umafika pansi

(b) liwiro la mpira ukagunda pansi

(c) mtunda wopingasa womwe mpira ungafikire umayesedwa kuchokera m'mphepete mwa nyumbayo

(d) kutalika kwakukulu komwe mpirawo ungafikire

yankho;

Choyamba, timawerengera gawo loyima (v _oy ) ndi gawo lopingasa (v _ox ) la liwiro loyambirira (v _o ).

v _ox = vo _o cos 30 ^o = (10 m/s)(0.87) = 8.7 m/s

v _oy = vo _o sin 30 ^o = (10 m/s)(0.5) = 5 m/s

a) Nthawi yomwe mpira umafika pansi

Yankho lake lili ngati kudziwa nthawi (t) molunjika mmwamba molunjika. Kukula kwa vekitala yomwe imayang'ana mmwamba kumasankhidwa kukhala kwabwino, kukula kwa vekitala yomwe imayang'ana pansi kumasankhidwa kukhala kwabwino. Malo a mpira pomwe amaponyedwa amasankhidwa ngati malo ofotokozera. h ndi yoipa chifukwa pamwamba pa nthaka pali pansi pa malo ofotokozera, g ndi yoipa chifukwa njira yofulumira ya mphamvu yokoka ndi yotsika.

Zodziwika:

v _oy = 5 m/s, h = – 5 m, g = – 9.8 m/s ²

Ankafuna: t

h = vot ₊ ½ gt ²

-5 = 5 t + ½ (-9.8) t ²

-5 = 5 t – 4.9 t ²

-4.9 t ² + 5 t + 5 = 0

Gwiritsani ntchito fomula ya quadratic:

Nthawi mumlengalenga = nthawi yopuma kuyambira pomwe mpira unaponyedwa kuti ufike pansi = masekondi 1.64.

b) Liwiro la mpira ukagunda pamwamba pa nthaka

v _tx = v _ng'ombe = v _x = 8.7 m/s

v _ty = ?

Choyamba, timawerengera liwiro lomaliza molunjika (v _ty ). Yankho lake lili ngati kudziwa liwiro lomaliza poyenda molunjika mmwamba.

Yodziwika: v _oy = 5 m/s, g = -9.8 m/s ² , t = 1.64 masekondi

Akufuna: v _ty

v _ty = v _oy + gt

v _ty = 5 + (-9.8)(1.64)

v _ty = 5 – 16

v _ty = -11 m/s

Chizindikiro choyipa chimasonyeza kuti njira yopita patsogolo kwa liwiro lomaliza ndi yotsika.

Liwiro la chipolopolo chikagunda pansi:

Kulunjika kwa liwiro la chipolopolo = komwe chipolopolocho chikuyenda chikagunda pansi:

Liwiro la chipolopolo chikagunda pansi:

Chifukwa vtx ili moyang'anizana ndi x-axis yabwino (kumanja) ndipo vty ili moyang'anizana ndi y-axis yoyipa (pansi),

komwe chipolopolocho chikupita chikagunda pansi ndi -52o pafupifupi x-axis yabwino (onani chithunzi pansipa).

c) Mtunda wopingasa womwe mpira ungafikire umayesedwa kuchokera m'mphepete mwa nyumbayo

Yankho lake lili ngati kudziwa mtunda woyenda (d) pa kayendedwe kofanana kolunjika.

Kudziwika: t = masekondi 1.64, v _x = 8.7 m/s

Ankafuna: d

d = vt = (8.7 m/s)(1.64 s) = 14.3 m

d) Kutalika kwakukulu komwe mpira ungafikire

Zodziwika: v _oy = 5 m/s, v _ty = 0 m/s ( gawo loyima la liwiro pa kutalika kwakukulu = 0 m/s), g = -9.8 m/s ².

Ankafuna: h

v _ty ² = v _oy ² + 2 gh

0 m/s = (5 m/s) ² + 2(-9.8 m/s ² )(h)

0 m/s = 25 (m/s) ² + (-19.6 m/s ² )(h)

25 (m/s) ² = -19.6 m/s 2 (h)

h = 25 (m/s) ² : -19.6 m/s ² = 1.3 mamita

Kutalika kwakukulu komwe mpira ungafikire = mamita 1.3 pamwamba pa nyumba = 1.3 m + 50 m = mamita 51.3 pamwamba pa nthaka.