Ka neʻe ʻana o ka papahana

ʻAtikala e pili ana i ka neʻe ʻana o ka Projectile a me nā pilikia laʻana me nā hoʻonā

Ka wikiwiki mua (v_o) a me ka ʻāpana o ka wikiwiki mua (v_ox a me v_oy)

He mea nona nā neʻe parabolic e loaʻa mau ana ka wikiwiki mua. No ka mea, ʻo ka neʻe parabolic ka hui pū ʻana o nā neʻe ma nā kuhikuhi ʻaoʻao a me nā kuhikuhi kū, aia pū kekahi mau ʻāpana ʻaoʻao a me nā ʻāpana kū i ka wikiwiki mua.

Inā neʻe parabolical ka mea e like me nā Kiʻi 1 a me 3 a laila ua helu ʻia ka wikiwiki mua ma ke kuhikuhi ākea (v _ox ) a me ka wikiwiki mua ma ke kuhikuhi kū pololei (v _oy ) me ka hoʻohana ʻana i ka hoohalike:

v _ox = v _o cos θ

v _oy = v _o sin θ

Inā e neʻe ana ka mea ma ke ʻano parabolic e like me ke kiʻi 2 a laila v _o = v _ox (v _oy = 0)

Ka wikiwiki (v_x a me v_y) a me ke Kūlana (x a me y)

Hoʻomaulia ʻia ka wikiwiki ma nā kuhikuhi ʻaoʻao a me ke kū pololei i kekahi manawa me ka hoʻohana ʻana i ka hoohalike:

v _x = v _ox = mau ( neʻe laina like )

v _y = v _oy + gt a i ʻole v _y ² = v _oy ² + 2 gh (neʻe hāʻule manuahi)

Ua helu ʻia ke kūlana o nā mea ma nā kuhikuhi ʻaoʻao (x) a me ke kuhikuhi ʻaoʻao (y) ma kahi manawa i hoʻohana ʻia me ka hoʻohālikelike:

x = v _ox t

y = v _oy t + 1/2 gt ^​​2

Ka hopena o ka wikiwiki (v) a me ke kūlana (h)

Ua helu ʻia ka wikiwiki hopena ma kahi manawa i kuhikuhi ʻia me ka hoʻohana ʻana i ka hoohalike:

Hoʻomaulia ʻia ke kuhikuhi o nā mea ma kahi manawa kikoʻī me ka hoʻohana ʻana i ka hoohalike:

Notes:

1. Ua manaʻo ʻia ka ʻāpana pae o ka neʻe parabolic ʻo ia ka neʻe linear like, no laila ʻo vox = vx mau nō ia

2. ʻO ka ʻāpana kū pololei o ka neʻe parabolic i manaʻo ʻia he neʻe hāʻule manuahi, no laila inā neʻe ka mea i ka parabolic, e like me nā Kiʻi 1 a me 3, ʻo ka ʻāpana kū pololei o ka wikiwiki o ka mea ma ke kiʻekiʻe loa he zero (v _y = 0). Inā ʻoe e hoʻolei i kahi kinikini i luna i kahi kiʻekiʻe loa, e hoʻomaha ka mea no kekahi manawa (v _y = 0) ma mua o ka huli ʻana i lalo. No laila, ʻo ka wikiwiki o ka mea e hoʻoneʻe ana i ka parabolic ma ke kiʻekiʻe loa = v _x = v _ox

3. Inā neʻe parabolic ka mea e like me ka mea i hōʻike ʻia ma ke Kiʻi 2, ʻo ka ʻāpana kū pololei o ka neʻe parabolic e nānā ʻia ʻo ia ka neʻe hāʻule manuahi. Inā neʻe parabolic ka mea e like me nā Kiʻi 1 a me 3 a laila ʻo ka ʻāpana kū pololei o ka neʻe parabolic e nānā ʻia ʻo ia ka neʻe kū i luna.

Nā pilikia laʻana:

1. Ua pana ʻia kahi pōkā ma kahi ʻaoʻao pālahalaha me ka wikiwiki mua o 20 m/s. Inā he 5 mika ka pū ma luna o ka honua, e hoʻoholo:

(a) ka manawa ma ka lewa

(b) ke kiʻekiʻe loa

(c) ka mamao pae

(d) ka wikiwiki o ka pōkā i kona wā e pā ai i ka honua

pāʻoihana:

Hoʻopili ʻia ka neʻe ʻana ma ke kuhikuhi ʻākea e like me ka neʻe laina like, ʻoiai ua hoʻopili ʻia ka neʻe ʻana ma ke kuhikuhi kū pololei e like me ka neʻe hāʻule manuahi.

ʻIke ʻia:

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

a) Ka manawa ma ka lewa

ʻO ka hopena e like me ka hoʻoholo ʻana i ka manawa manawa (t) ma ka neʻe hāʻule manuahi.

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

Makemake ʻia: t

b) Ke kiʻekiʻe loa

Ke kiʻekiʻe loa = h = 5 mika.

c) Ka mamao pae (d)

Ua like ka hopena me ka hoʻoholo ʻana i ka mamao ma ka neʻe linear like

ʻIke ʻia: v _ox = 20 m/s, t = 1 kekona

Makemake ʻia: d

d = vt

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

d) Ka wikiwiki i ka wā e pā ai ka pōkā i ka honua

v _tx = v _ox = 20 m/s

v _ty = ?

ʻO ka mea mua, helu mākou i ka wikiwiki hope loa ma ke kuhikuhi kū pololei (vty). Ua like ka hopena me ka hoʻoholo ʻana i ka wikiwiki hope loa o ka neʻe hāʻule manuahi.

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

Makemake ʻia: v _ty

vt ₌ v _o + gt —> vo = 0

vt = _gt

vt ₌ (9.8 m/s² ⁾ (1 s)

vt = 9.8 m/ _s

ʻO ka wikiwiki o ka pōkā i kona wā e pā ai i ka honua:

Ke kuhikuhi o ka pōkā:

No ka mea, aia ʻo v _tx ma ke kuhikuhi o ka axis-x maikaʻi (ma ka ʻākau) a aia ʻo v _ty ma ke kuhikuhi o ka axis-y maikaʻi ʻole (i lalo),

ʻO ke kuhikuhi o ka pōkā i kona pā ʻana i ka honua he -26.1 ^o i ka axis-x maikaʻi (e nānā i ke kiʻi ma lalo).

2. Ua kī aku ka pūkuniahi i kahi pōkā ma 30 ^o i ka pae me ka wikiwiki o 60 m/s. E hoʻoholo:

(a) ke kiʻekiʻe loa

(b) ka wikiwiki o ka pōkā ma ke kiʻekiʻe loa

(c) ka manawa ma ka lewa

(d) ka mamao pae

(e) ka wikiwiki o ka pōkā i kona pā ʻana i ka honua. Manaʻo ʻia he pālahalaha ka honua. 🙂

pāʻoihana:

Hoʻopili ʻia ka neʻe ʻana ma ke kuhikuhi ʻākea e like me ka neʻe laina like, hoʻopili ʻia ka neʻe ʻana ma ke kuhikuhi kū e like me ka neʻe ʻana i luna.

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

Ma muli o ka ʻikepili i ʻike ʻia, helu mua mākou i nā ʻāpana kū pololei (vo _oy ) a me ka pae (v _ox ) o ka wikiwiki mua (v _o ).

a) Ke kiʻekiʻe loa (h)

Ua like ka hopena me ka hoʻoholo ʻana i ke kiʻekiʻe loa ma ka neʻe ʻana i luna a kū pololei.

ʻIke ʻia:

v _ox = v _o cos θ = (60)(cos 30) = (60)(0.87) = 52 m/s

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

a) Kiʻekiʻe loa (h)

Ua like ka hopena me ka hoʻoholo ʻana i ke kiʻekiʻe loa ma ka neʻe ʻana i luna me ke kū pololei.

ʻIke ʻia:

v _oy = 30 m/s (ʻo kēia ka wikiwiki mua o ka pōkā)

v _ty = 0 m/s (Ma ke kiʻekiʻe loa, ʻo ka wikiwiki kū pololei o ka pōkā = 0 m/s. ʻO kēia ka wikiwiki hope loa.)

g = – 9.8 m/s ²

Makemake ʻia: h

vt ₂ = v _o ^{2 + 2} gh

0 ² = 30 ² + 2 (-9.8) h

0 = 900 – 19.6 hola

900 = 19.6 hola

h = 900 / 19.6

h = 45.9 mika

ʻO ke kiʻekiʻe loa i loaʻa e ka pōkā = 45.9 mika.

b) Ka wikiwiki ma ke kiʻekiʻe loa

Ma ke kiʻekiʻe loa, ʻo ka wikiwiki ma ke kuhikuhi kū pololei = 0 m/s. Ma ke kiʻekiʻe loa, ʻo ia wale nō ka wikiwiki ma ke kuhikuhi ākea. ʻO ka wikiwiki ma ke kuhikuhi ākea ma ke kiʻekiʻe loa e like me ka wikiwiki mua ma ke kuhikuhi ākea, ʻo ia hoʻi he 52.2 m/s. ʻO ke kuhikuhi o ka wikiwiki ma ke kuhikuhi ākea e mau ana, ʻo ia hoʻi, ma ke kuhikuhi o ka axis x maikaʻi (inā ua wehewehe ʻia ka neʻe ʻana o kahi mea ma ke kiʻikuhi ma luna).

c) Ka manawa ma ka lewa

Ua like ka hopena me ka hoʻoholo ʻana i ka manawa (t) i ke kūkākūkā ʻana o ka neʻe ʻana i luna i luna.

ʻIke ʻia:

v _oy = 30 m/s (ʻo kēia ka wikiwiki mua o ka pōkā ma ke kuhikuhi kū pololei)

g = – 9.8 m/s ²

h = 0 m (ke hoʻi ka pōkā i ka honua, ʻo ka neʻe ʻana o ka pōkā ma ke kuhikuhi kū pololei = 0 m)

Makemake ʻia: t

h = v _o t + ½ gt ²

0 = (30) t + ½ (-9.8 m/ ^s² ) ^t²

0 = (30) t – 4.9 t ²

(30) t = 4.9 t ²

30 = 4.9 t

t = 30 / 4.9

t = 6.12 kekona

Ka manawa ma ka lewa = 6.12 kekona

d) Ka mamao pae (d)

Ua like ka hopena me ka hoʻoholo ʻana i ka mamao (d) ma ka neʻe laina like.

ʻIke ʻia:

v _ox = 52.2 m/s

t = 6.12 kekona

Makemake ʻia: d

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

e) Ka wikiwiki i ka wā e pā ai ka pōkā i ka honua

v _tx = v _ox = 52.2 m/s

v _ty = ?

ʻO ka mea mua, helu mākou i ka wikiwiki hope loa ma ke kuhikuhi kū pololei (v _ty ). ʻO ka hopena, ʻo ia ka hoʻoholo ʻana i ka wikiwiki hope loa ma ka neʻe kū pololei i luna.

Makemake ʻia: v _oy = 30 m/s, g = -9.8 m/s ² , t = 6.12 kekona

Makemake ʻia: v _ty

v _ty = v _oy + gt

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

v _ty = (30) – (60)

v _ty = -30 m/s

Hōʻike kahi hōʻailona maikaʻi ʻole ua iho ke kuhikuhi o ka wikiwiki hope loa. E hoʻomaopopo he like ka wikiwiki mua ma ke kuhikuhi kū pololei me ka wikiwiki hope loa ma ke kuhikuhi kū pololei.

ʻO ka wikiwiki o ka pōkā i kona wā e pā ai i ka honua:

Ke kuhikuhi o ka pōkā:

ʻOiai ʻo vtx _ma ke kuhikuhi o ka axis-x maikaʻi (ma ka ʻākau) a ʻo vty ma ke kuhikuhi o ka axis-y maikaʻi ʻole (i lalo),

ʻO ke kuhikuhi o ka wikiwiki o ka pōkā i kona pā ʻana i ka honua he -30 ^o e pili ana i ka axis-x maikaʻi (e nānā i ke kiʻi ma lalo).

3. Ua kiola ʻia kahi pōpō mai ka lihi o kahi hale he 50 mika ke kiʻekiʻe me ka wikiwiki mua o 10 m/s. Inā ua kiola ʻia ka pōpō ma 30o ma kahi o ka pae, e hoʻoholo:

(a) ka manawa i hiki ai ka pōpō i ka honua

(b) ka wikiwiki o ka pōpō i kona kuʻi ʻana i ka honua

(c) ua ana ʻia ka mamao ākea e hiki ai i ka pōpō mai ka lihi o ka hale

(d) ke kiʻekiʻe loa i hiki i ka pōpō

pāʻoihana:

ʻO ka mea mua, helu mākou i ka ʻāpana kū pololei (vo _oy ) a me ka ʻāpana moe (v _ox ) o ka wikiwiki mua (v _o ).

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

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

a) Ka manawa i hiki ai ka pōpō i ka honua

Ua like ka hopena me ka hoʻoholo ʻana i ka manawa manawa (t) i kahi neʻe kū pololei i luna. Ua koho ʻia ka nui o ka vector nona ke kuhikuhi i luna e maikaʻi, ua koho ʻia ka nui o ka vector nona ke kuhikuhi i lalo e maikaʻi ʻole. Ua koho ʻia ke kūlana pōpō kahi i hoʻolei ʻia ai ma ke ʻano he kiko kuhikuhi. He maikaʻi ʻole ʻo h no ka mea aia ka ʻili honua ma lalo o ke kiko kuhikuhi, he maikaʻi ʻole ʻo g no ka mea aia ke kuhikuhi o ka wikiwiki o ka umekaumaha i lalo.

ʻIke ʻia:

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

Makemake ʻia: t

h = v _o t + 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

E hoʻohana i ke ʻano quadratic:

Ka manawa ma ka lewa = ka manawa mai ka hoʻolei ʻia ʻana o ka pōpō a hiki i ka honua = 1.64 kekona.

b) Ka wikiwiki o ka pōpō i kona wā e pā ai i ka ʻili o ka honua

v _tx = v _ox = v _x = 8.7 m/s

v _ty = ?

ʻO ka mea mua, helu mākou i ka wikiwiki hope loa ma ke kuhikuhi kū pololei (v _ty ). Ua like ka hopena me ka hoʻoholo ʻana i ka wikiwiki hope loa ma ka neʻe kū pololei i luna.

ʻIke ʻia: v _oy = 5 m/s, g = -9.8 m/s ² , t = 1.64 kekona

Makemake ʻia: v _ty

v _ty = v _oy + gt

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

v _ty = 5 – 16

v _ty = -11 m/s

Hōʻike ka hōʻailona maikaʻi ʻole e iho ana ke kuhikuhi o ka wikiwiki hope loa.

ʻO ka wikiwiki o ka pōkā i kona wā e pā ai i ka honua:

ʻO ke kuhikuhi o ka wikiwiki o ka pōkā = ke kuhikuhi o ka neʻe ʻana o ka pōkā i kona wā e pā ai i ka honua:

ʻO ka wikiwiki o ka pōkā i kona wā e pā ai i ka honua:

No ka mea, aia ʻo vtx ma ke kuhikuhi o ka axis-x maikaʻi (ma ka ʻākau) a aia ʻo vty ma ke kuhikuhi o ka axis-y maikaʻi ʻole (i lalo),

ʻO ke kuhikuhi o ka pōkā i kona pā ʻana i ka honua he -52o e pili ana i ka axis x maikaʻi (e nānā i ke kiʻi ma lalo).

c) Ua ana ʻia ka mamao pālahalaha e hiki ai i ka pōpō mai ka lihi o ka hale

Ua like ka hopena me ka hoʻoholo ʻana i ka mamao i hele ʻia (d) ma ka neʻe laina like.

ʻIke ʻia: t = 1.64 kekona, v _x = 8.7 m/s

Makemake ʻia: d

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

d) ʻO ke kiʻekiʻe loa i hiki i ka pōpō

ʻIke ʻia: v _oy = 5 m/s, v _ty = 0 m/s ( ʻāpana kū pololei o ka wikiwiki ma ke kiʻekiʻe loa = 0 m/s), g = -9.8 m/s ².

Makemake ʻia: 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 mika

ʻO ke kiʻekiʻe loa i hiki i ka pōpō = 1.3 mika ma luna o ka piko o ka hale = 1.3 m + 50 m = 51.3 mika ma luna o ka ʻili honua.