Nā nīnau hoʻohālike vector

25 mau laʻana o nā pilikia Vector

1. ʻElua mau mana e kū pono ana kekahi i kekahi, ʻo kēlā me kēia me ka nui o 3 N a me 4 N. ʻO ka nui o ka hopena o nā mana ʻelua...
Pahana
Ua ʻike ʻia:
F₁ = 3 N, F₂ = 4 N
Nīnau: He aha ka hopena o nā vectors ʻelua?
Pane:
ʻElua wale nō vectors a ua kū pololei nā vectors ʻelua kekahi i kekahi no laila hoʻohana ka hopena i ke ʻano Pythagorean.
2. Inā ʻo ka nui o ka vector A = 4 mau ʻāpana, hana ia i kahi kihi o 30^o me ka axis-x maikaʻi, a laila ʻo ka nui o ka vector ma ka axis-x a me ka axis-y he...
Pahana
Ua ʻike ʻia:
A = 4 mau ʻāpana, Huina = 30^o
Nīnau ʻia: A_x a me A_y ?
Pane:
3. ʻElua mau vectors ikaika F₁ a me F₂ ʻO kēlā me kēia me ka nui o 5 N a me 12 N, nona ke kiko like o ka hoʻopili ʻana a e pili ana kekahi i kekahi ma ke kihi o 60°, ʻo ka waiwai hopena o nā vectors ʻelua he...
Pahana
Ua ʻike ʻia:
F₁ = 5 N, F₂ = 12 N, kihi = 60^o
Nīnau: He aha ka hopena o nā vectors ʻelua?
Pane:
ʻElua wale nō vectors a ʻaʻole kū pololei nā vectors ʻelua kekahi i kekahi (aia lākou ma ke kihi o 60° kekahi i kekahi).^o) no laila ke hoʻohana nei ka hopena o ka pilikia i ke ʻano cosine.
4. ma₁ = 20 mau ʻāpana a me v₂ = 20 mau ʻāpana. Pehea ka nui o ka vector hopena?

Pahana
Ke helu nei i ka vector ʻāpana:
v_1x = v₁ ka helu 30^o = (20)(½√3) = -10√3
v_1y = v₁ hewa 30^o = (20)(½) = 10
v_2x = v₂ ka helu 30^o = (20)(½√3) = 10√3
v_2y = v₂ hewa 30^o = (20)(½) = 10

v_x = v₁x + v₂x = -10√3 + 10√3 = 0
v_y = v₁y + v₂y = 10 + 10 = 20

Wehewehe: v_1x hōʻailona maikaʻi ʻole ma muli o ke kuhikuhi o v_1x i ka hema, ma ke axis x maikaʻi ʻole. v_2x he maikaʻi no ka mea aia ke kuhikuhi i ka ʻākau a i ʻole ma ke kuhikuhi o ka axis-x maikaʻi. v_1y a me v_2y he maikaʻi no ka mea ʻo kona kuhikuhi i luna ma ke kuhikuhi o ka axis-y maikaʻi. No ka ʻike ʻana i ke kuhikuhi o kēlā me kēia vector component a inā he maikaʻi a maikaʻi ʻole paha ka vector component, e kahakiʻi i ka vector component ma ka axis-x a me ka axis-y e like me ka mea i hōʻike ʻia ma ka laʻana nīnau helu 2.

Ke helu nei i ka vector hopena:
ʻO ka nui o ka vector hopena he 20 mau ʻāpana

5. Holo kekahi keiki i kahi mamao o 80 m i ke kūkulu ʻākau, a laila huli i ka hikina he 80 m a i ka hema he 20 mika. ka neʻe ʻana ka mea a ke keiki i hana ai...

A. 60 m
B. 80 m
C. 100 m
D. 120 m
E. 180 m

Pahana

Vector hoʻoneʻe

E hoʻohana i ke ʻano hana Pythagorean:
Hikina ʻĀkau
ʻO C ka pane pololei

6. Hele ʻo Budi i 6 mika i ka hikina, a laila 6 mika i ka hema, a me 2 mika i ka hikina. ʻO ka neʻe ʻana o Budi mai kona kūlana hoʻomaka he...

A. 20 m
B. 14 m
C. 12 m
D. 10 m
E. 8 m

Pahana

E hoʻohana i ke ʻano hana Pythagorean:

Ke kuhikuhi hikina hema
ʻO D ka pane pololei.

7.

ʻO ka hopena o nā mana ʻekolu ma ke kiʻi ma ka ʻaoʻao he…

A. 24 N
B. 16 N
C. 12 N
D. 10 N
E. 4 N

Pahana
Ua ʻike ʻia :
F₁ = 20 Newton, Huina ma waena o F₁ a ʻo ke axis-x = 0
F₂ = 20 Newton, Huina ma waena o F₂ a ʻo ke axis-x = 60
F₃ = 24 Newton, Huina ma waena o F₃ a ʻo ke axis-x = 60
Ua nīnau ʻia : ʻO ka hopena o nā mana ʻekolu (F₁, F₂ a me F₃)
Pane :

Nā ʻāpana o ka vector ikaika ma nā axis x a me y
F_1x = (F₁)(cos 0) = (20)(1) = 20. Maikaʻi no ka mea aia ia ma ke kuhikuhi like me ke axis x maikaʻi (ma ka ʻākau)
F_1y = (F₁)(hewa 0) = (20)(0) = 0
F_2x = (F₂)(cos 60) = (20)(0,5) = -10. Maikaʻi ʻole no ka mea aia ia ma ke kuhikuhi like me ke axis x maikaʻi ʻole (ma ka hema)
F_2y = (F₂)(sin 60) = (20)(0,5√3) = 10√3. Maikaʻi no ka mea aia ia ma ke kuhikuhi like me ke axis y maikaʻi (i luna)
F_3x = (F₃)(cos 60) = (24)(0,5) = -12. Maikaʻi ʻole no ka mea aia ia ma ke kuhikuhi like me ke axis x maikaʻi ʻole (ma ka hema)
F_3y = (F₃)(sin 60) = (24)(0,5√3) = -12√3. Maikaʻi ʻole no ka mea aia ia ma ke kuhikuhi like me ke axis y maikaʻi ʻole (i lalo)
ʻO ka hopena o nā ʻāpana vector ikaika ma nā axis x a me y
F_x =F_1x - F_2x - F_3x = 20 – 10 – 12 = -2
F_y =F_1y +F_2y - F_3y = 0 + 10√3 – 12√3 = -2√3
ʻO ke kolu o ka hopena ka nui vector e haʻi
ʻO ka pane pololei ʻo E.

8.

ʻO ka vector ikaika F₁, F₂, a me F₃ aia ma ka kiʻikuhi Cartesian e like me ka mea i hōʻike ʻia ma ke kiʻi:
ʻO ka hopena o nā vectors ʻekolu he…

A. √26 ʻĀkau
B. √76 ʻĀkau
C. √84 ʻĀkau
D. √168 ʻĀkau
E. √204 ʻĀkau

Pahana
Ua ʻike ʻia :
F₁ = 12 Newton, Huina ma waena o F₁ a ʻo ke axis-x = 30
F₂ = 10 Newton, Huina ma waena o F₂ a ʻo ke axis-x = 90
F₃ = 8 Newton, Huina ma waena o F₃ a ʻo ke axis-x = 30
Ua nīnau ʻia : ʻO ka hopena o nā vectors ikaika ʻekolu (F₁, F₂ a me F₃)
Pane :
Nā ʻāpana o ka vector ikaika ma nā axis x a me y
F_1x = (F₁)(cos 30) = (12)(0,5√3) = 6√3. Maikaʻi no ka mea aia ia ma ke kuhikuhi like me ke axis x maikaʻi (ma ka ʻākau)
F_1y = (F₁)(sin 30) = (12)(0,5) = 6. Maikaʻi no ka mea aia ia ma ke kuhikuhi like me ke axis y maikaʻi (i luna)
F_2x = (F₂)(cos 90) = (10)(0) = 0.
F_2y = (F₂)(sin 90) = (10)(1) = -10. Maikaʻi ʻole no ka mea aia ia ma ke kuhikuhi like me ke axis y maikaʻi ʻole (i lalo)
F_3x = (F₃)(cos 30) = (8)(0,5√3) = -4√3. Maikaʻi ʻole no ka mea aia ia ma ke kuhikuhi like me ke axis x maikaʻi ʻole (ma ka hema)
F_3y = (F₃)(sin 30) = (8)(0,5) = -4. Maikaʻi ʻole no ka mea aia ia ma ke kuhikuhi like me ke axis y maikaʻi ʻole (i lalo)
ʻO ka hopena o nā ʻāpana vector ikaika ma nā axis x a me y
F_x =F_1x +F_2x - F_3x = 6√3 + 0 – 4√3 = 2√3
F_y =F_1y - F_2y - F_3y = 6 – 10 – 4 = -8
Ka hopena o nā vectors ikaika ʻekolu
ʻO ka pane pololei ʻo B.

9. E nānā i ke kiʻi ma ka ʻaoʻao. ʻO ka nui o ka hopena o nā mana ʻekolu…
H. 0
B. 2√3 N
C. 4√3 N
D. 8√3 N
E. 12√3 N
Pahana
Ua ʻike ʻia :
F₁ = 4 Newton, Huina ma waena o F₁ a ʻo ke axis-x = 30
F₂ = 6√3 Newton, Huina ma waena o F₂ a ʻo ke axis-x = 0
F₃ = 2 Newton, Huina ma waena o F₃ a ʻo ke axis-x = 90
Ua nīnau ʻia : Ka nui o ka hopena o nā mana ʻekolu (F₁, F₂ a me F₃)
Pane :
Nā ʻāpana o ka vector ikaika ma nā axis x a me y
F_1x = (F₁)(cos 30) = (4)(0,5√3) = 2√3. Maikaʻi no ka mea aia ia ma ke kuhikuhi like me ke axis x maikaʻi (ma ka ʻākau)
F_1y = (F₁)(sin 30) = (4)(0,5) = 2. Maikaʻi no ka mea aia ia ma ke kuhikuhi like me ke axis y maikaʻi (i luna)
F_2x = (F₂)(cos 0) = (6√3)(1) = -6√3. Maikaʻi ʻole no ka mea aia ia ma ke kuhikuhi like me ke axis x maikaʻi ʻole (ma ka hema)
F_2y = (F₂)(hewa 0) = (6√3)(0) = 0.
F_3x = (F₃)(cos 90) = (2)(0) = 0.
F_3y = (F₃)(sin 90) = (2)(1) = -2. Maikaʻi ʻole no ka mea aia ia ma ke kuhikuhi like me ke axis y maikaʻi ʻole (i lalo)
ʻO ka hopena o nā ʻāpana vector ikaika ma nā axis x a me y
F_x =F_1x - F_2x +F_3x = 2√3 – 6√3 + 0 = -4√3
F_y =F_1y +F_2y - F_3y = 2 + 0 – 2 = 0
Ka hopena o nā vectors ikaika ʻekolu
ʻO C ka pane pololei.

10. Hele pololei kekahi keiki i 10 mika i ke komohana, a laila huli i ka hema no 4 mika, a huli hou i ka hikina no 13 mika. ʻO ka neʻe ʻana o ke keiki mai ke kūlana mua he...
A. 4 mika ma ke komohana hema
B. 5 mika hema
C. 5 mika hikina hema
D. 10 mika hikina
E. 10 mika hikina hema

Pahana

ʻO C ka pane pololei.

11. ʻO ka hopena o nā mana ʻekolu ma ke kiʻi ma ka ʻaoʻao he…

A. 1,0 N
B. 1,5 N
C. 1,9 N
D. 2,0 N
E. 2,3 N
Pahana
E helu i ka nui o kēlā me kēia vector ʻāpana:
F_1x = 10 N
F_1y = 0
F_2x = -10 cos 60 = – (10)(0,5) = – 5 N
F_2y = 10 hewa 60 = (10)(0,87) = 8,7 N
F_3x = -12 cos 60 = – (12)(0,5) = – 6 N
F_3y = -12 hewa 60 = – (12)(0,87) = – 10,4 N
E hoʻoholo i ka vector hopena:

12. Ua hōʻike ʻia ʻekolu mau vectors o kahi kiko hoihoi ma ke kiʻi. ʻO ka nui o kēlā me kēia vector:
|V₁ | = 30 mau ʻāpana
|V₂ | = 30 mau ʻāpana
|V₃ | = 40 mau ʻāpana
ʻO ka nui o ka hopena o nā vectors ʻekolu he...
A. 30 mau ʻāpana
B. 40 mau ʻāpana
C. 50 mau ʻāpana
D. 90 mau ʻāpana
E. 110 mau ʻāpana
Pahana
Ua ʻike ʻia:
V₁ = 30, Huina ma waena o V₁ a ʻo ke axis-x = 30^o
V₂ = 30, Huina ma waena o V₂ a ʻo ke axis-x = 30^o
V₃ = 40, Huina ma waena o V₃ a ʻo ke axis-x = 0^o
Nīnau: ʻO ka hopena o nā vectors ʻekolu (V₁, V₂ a me V₃)
Pane:
Nā ʻāpana o ka vector ikaika ma nā axis x a me y
V_1x = (V₁)(cos 30^o) = (30)(0,5√3) = 15√3. Maikaʻi no ka mea aia ia ma ke kuhikuhi like me ka axis-x maikaʻi (ma ka ʻākau)
V_1y = (V₁)(hewa 30^o) = (30)(0,5) = 15. Maikaʻi no ka mea aia ia ma ke kuhikuhi like me ka axis-y maikaʻi (i luna)
V_2x = (V₂)(cos 30^o) = (30)(0,5√3) = -15√3. Maikaʻi ʻole no ka mea aia ia ma ke kuhikuhi like me ka axis-x maikaʻi ʻole (ma ka hema)
V_2y = (V₂)(hewa 30^o) = (30)(0,5) = 15. Maikaʻi no ka mea aia ia ma ke kuhikuhi like me ka axis-y maikaʻi (i luna)
V_3x = (V₃)(cos 0^o) = (40)(1) = 40. Maikaʻi no ka mea aia ia ma ke kuhikuhi like me ka axis-x maikaʻi (ma ka ʻākau)
V_3y = (V₃)(hewa 0^o) = (40)(0) = 0

13. ʻElua mau mana (kahi kiko o ka hoʻopili ʻana) e kū pololei ana kekahi i kekahi, ʻo ko lākou nui he 12 N a me 5 N. ʻO ka nui o ka hopena o nā mana ʻelua…
A. 17 N
B. 15 N
C. 13 N
D. 9 N
E. 7 N
Pahana
Ua ʻike ʻia:
Kaila 1 (F₁) = 12 Newton
Kaila 2 (F₂) = 5 Newton
Makemake ʻia: Ka hopena o nā ikaika ʻelua (ΣF)
Pane:
Ua kū pololei nā mana ʻelua kekahi i kekahi no laila ua helu ʻia ka ikaika hopena me ka hoʻohana ʻana i ke ʻano Pythagorean.

14. Ua hōʻike ʻia ʻekolu mau vectors o kahi kiko hoihoi ma ke kiʻi ma lalo nei. ʻO ka nui o kēlā me kēia vector:
|V₁| = 30 mau ʻāpana
|V₂| = 30 mau ʻāpana
|V₃| = 40 mau ʻāpana
ʻO ka nui o ka hopena o nā vectors ʻekolu he...
A. 30 mau ʻāpana
B. 40 mau ʻāpana
C. 50 mau ʻāpana
D. 90 mau ʻāpana
E. 110 mau ʻāpana
Pahana
Ua ʻike ʻia:
v₁ = 30 mau ʻāpana, e hana ana i kahi kihi o 30^o i ka axis-x maikaʻi ʻole.
v₂ = 30 mau ʻāpana, e hana ana i kahi kihi o 30^o i ka axis-x maikaʻi.
v₃ = 40 mau ʻāpana, e hana ana i kahi kihi o 0^o i ka axis-x maikaʻi.
Nīnau ʻia: Vector hopena
Pane:
E helu i nā ʻāpana vector:
v_1x = v₁ ka helu 30^o = (30)(0,5√3) = -15√3 (hōʻailona maikaʻi ʻole no ka mea aia ia ma ke kuhikuhi like me ka axis-x maikaʻi ʻole)
v_1y = v₁ hewa 30^o = (30)(0,5) = 15 (hōʻailona maikaʻi no ka mea aia ia ma ke kuhikuhi like me ka axis-y maikaʻi)
v_2x = v₂ ka helu 30^o = (30)(0,5√3) = 15√3 (hōʻailona maikaʻi no ka mea aia ia ma ke kuhikuhi like me ka axis-x maikaʻi)
v_2y = v₂ hewa 30^o = (30)(0,5) = 15 (hōʻailona maikaʻi no ka mea aia ia ma ke kuhikuhi like me ka axis-y maikaʻi)
v_3x = v₃ ka helu 0^o = (40)(1) = 40 (hōʻailona maikaʻi no ka mea aia ia ma ke kuhikuhi like me ka axis-x maikaʻi)
v_3y = v₃ hewa 0^o = (40)(0) = 0

15. ʻO ka hopena o nā mana ʻekolu ma ke kiʻi ma lalo nei...
A. 0 N
B. 2 N
C. 2√3 N
D. 3 N
E. 3√3 N
Pahana
Ua ʻike ʻia:
F₁ = 3 Hoʻokumu nā Newton i kahi kihi o 60^o i ka axis-x maikaʻi
F₂ = 3 Hoʻokumu nā Newton i kahi kihi o 0^o i ka axis-x maikaʻi ʻole
F₃ = 6 Hoʻokumu nā Newton i kahi kihi o 60^o i ka axis-y maikaʻi ʻole
Nīnau ʻia: Ka ikaika hopena
Pane:
E helu i ka vector ʻāpana:
F_1x =F₁ ka helu 60^o = (3)(0,5) = 1,5 N (hōʻailona maikaʻi no ka mea aia ia ma ke kuhikuhi o ka axis-x maikaʻi)
F_1y =F₁ hewa 60^o = (3)(0,5√3) = 1,5√3 N (hōʻailona maikaʻi no ka mea aia ia ma ke kuhikuhi o ka axis-y maikaʻi)
F_2x =F₂ ka helu 0^o = (3)(1) = -3 N (hōʻailona maikaʻi ʻole no ka mea aia ia ma ke kuhikuhi o ka axis-x maikaʻi ʻole)
F_2y =F₂ hewa 0^o = (3)(0) = 0
F_3x =F₃ ka helu 60^o = (6)(0,5) = 3 N (hōʻailona maikaʻi no ka mea aia ia ma ke kuhikuhi o ka axis-x maikaʻi)
F_3y =F₃ hewa 60^o = (6)(0,5√3) = -3√3 N (hōʻailona maikaʻi ʻole no ka mea aia ia ma ke kuhikuhi y-axis maikaʻi ʻole)

16. ʻElua mau vectors ikaika F₁ a me F₂ ʻO kēlā me kēia me ka nui o 15 N a me 9 N, nona ke kiko like o ka hoʻopili ʻana a e pili ana kekahi i kekahi ma ke kihi o 60°, ʻo ka waiwai hopena o nā vectors ʻelua he...
A. 15 N
B. 20 N
C. 21 N
D. 24 N
E. 30 N
Pahana
Ua ʻike ʻia:
Kaila 1 (F₁) = 15 Newton
Kaila 2 (F₂) = 9 Newton
Kihi (θ) = 60^o
Nīnau: Ka hopena o nā vectors ʻelua
Pane:
Aia ʻelua mau vectors e hana ana i kahi kihi o 60^o i hiki ai ke helu ʻia ka vector hopena me ka hoʻohana ʻana i ke ʻano cosine:

17. ʻO ka hopena o nā mana ʻekolu ma ke kiʻi ma ka ʻaoʻao he…
A. 24 N
B. 16 N
C. 12 N
D. 10 N
E. 4 N
Pahana
Ua ʻike ʻia:
F₁ = 20 Newton, Huina ma waena o F₁ a ʻo ke axis-x = 0
F₂ = 20 Newton, Huina ma waena o F₂ a ʻo ke axis-x = 60
F₃ = 24 Newton, Huina ma waena o F₃ a ʻo ke axis-x = 60
Nīnau: ʻO ka hopena o nā mana ʻekolu (F₁, F₂ a me F₃)
Pane:
Nā ʻāpana o ka vector ikaika ma nā axis x a me y
F_1x = (F₁)(cos 0) = (20)(1) = 20. Maikaʻi no ka mea aia ia ma ke kuhikuhi like me ka axis-x maikaʻi (ma ka ʻākau)
F_1y = (F₁)(hewa 0) = (20)(0) = 0
F_2x = (F₂)(cos 60) = (20)(0,5) = -10. Maikaʻi ʻole no ka mea aia ia ma ke kuhikuhi like me ka axis-x maikaʻi ʻole (ma ka hema)
F_2y = (F₂)(sin 60) = (20)(0,5√3) = 10√3. Maikaʻi no ka mea aia ia ma ke kuhikuhi like me ka axis-y maikaʻi (i luna)
F_3x = (F₃)(cos 60) = (24)(0,5) = -12. Maikaʻi ʻole no ka mea aia ia ma ke kuhikuhi like me ka axis-x maikaʻi ʻole (ma ka hema)
F_3y = (F₃)(sin 60) = (24)(0,5√3) = -12√3. Maikaʻi ʻole no ka mea aia ia ma ke kuhikuhi like me ka axis-y maikaʻi ʻole (i lalo)

18. Neʻe kekahi mea mai E a i F a pau ma G. ʻO ke kiʻi ma lalo nei, e hōʻike ana i ka neʻe ʻana o 10 mau anakahi, ʻo ia...

Pahana

Nā hoʻonohonoho kiko E = x, y = 1, 1

Nā hoʻonohonoho kiko F = x, y = 9, 1

Nā hoʻonohonoho kiko G = x, y = 9, 7

Ka lōʻihi o EF = 9-1 = 8

Ka lōʻihi o FG = 7-1 = 6

Ka lōʻihi o EG =

ʻO A ka pane pololei.

19. Holo kekahi kanaka ma ke kaʻa mai A a i B, he 30 km ma ka ʻākau, a laila hoʻomau i C, he 60 km ma ka hikina, a hōʻea hope loa i ke kūlanakauhale ʻo D, he 110 km ma ka hema. ʻO ka neʻe ʻana o ke kaʻa mai A a i D he...

A. 200 km

B. 140 km

C. 120 km

D. 100 km

Hikina 80 km

Pahana

ʻAA' = 60 km

A'D = 110 km – 30 km = 80 km

ʻO D ka pane pololei.

20. Ua holo ʻo Andi ma ke kaʻa mai ke kūlanakauhale A ma ka ʻākau a i ke kūlanakauhale B no 100 km, a laila hoʻomau i kāna huakaʻi i ke kūlanakauhale C ma ka hikina no 60 km, a laila hele ʻo Andi i ka hema a i ke kūlanakauhale D no 20 km. ʻO ka neʻe ʻana o ke kaʻa…

A. 10 km

B. 20 km

C. 80 km

D. 100 km

Hikina 180 km

Pahana

D'D = 60 km

AD' = 100 km – 20 km = 80 km

ʻO D ka pane pololei.

21. Ma ka hanana "City Marathon Festival" ma ʻOkakopa 2014 ma Jakarta he 4 mau māhele holo, ʻo ia hoʻi ka māhele piha marathon (42 km), mahele ka hapalua hapa (21 km), māhele 10 kilomita a me ka māhele 5 kilomita kahi i hoʻoholo ʻia ai ke ala no kēlā me kēia māhele. Hoʻomaka kēia heihei marathon mai ka Bung Karno Sports Complex a hoʻopau ma ka National Monument (Monas). Ua komo kekahi o nā mea komo i ka heihei, ʻo Andri, i ka heihei. piha marathon a hiki iā ia ke hele i ke ala mai nā wahi A, B, a me C wale nō e like me Kiʻi 2.

Inā hōʻike ka pahu 1 i 1 km, a laila ʻo ka neʻe holoʻokoʻa a Andri i hele ai…

A. 26 km

B. 20 km

C. 12 km

D. 10 km

Hikina 8 km

Pahana

ʻO ka lōʻihi o ka ʻaoʻao haʻahaʻa = 8 km, ʻo ka lōʻihi o ka ʻaoʻao mua = 6 km.

Ma ka hoʻohana ʻana i ke ʻano Pythagorean, Neʻe = R = 10 km

ʻO D ka pane pololei.

22. Holo kekahi kanaka ma ke kaʻa mai A a i B, he 30 km ma ka ʻākau, a laila hoʻomau i C, he 60 km ma ka hikina, a hōʻea hope loa i ke kūlanakauhale ʻo D, he 110 km ma ka hema. ʻO ka neʻe ʻana o ke kaʻa mai A a i D he...

A. 200 km

B. 140 km

C. 120 km

D. 100 km

Hikina 80 km

Pahana

ʻAA' = 60 km

A'D = 110 km – 30 km = 80 km

ʻO D ka pane pololei.

23. Ua holo ʻo Andi ma ke kaʻa mai ke kūlanakauhale A ma ka ʻākau a i ke kūlanakauhale B no 100 km, a laila hoʻomau i kāna huakaʻi i ke kūlanakauhale C ma ka hikina no 60 km, a laila hele ʻo Andi i ka hema a i ke kūlanakauhale D no 20 km. ʻO ka neʻe ʻana o ke kaʻa…

A. 10 km

B. 20 km

C. 80 km

D. 100 km

Hikina 180 km

Pahana

D'D = 60 km

AD' = 100 km – 20 km = 80 km

ʻO D ka pane pololei.

Vector Unit

24. Nā Nīnau Hoʻokolohua Lahui 2000/2001
Neʻe kahi mea i noho mua ma ke kiko kuhikuhi me ka wikiwiki v = (2i − 1,5h) ms^-1Ma hope o ka neʻe ʻana no 4 kekona, ua neʻe ka mea i kahi mamao o…
A. 2 m
B. 10 m
C. 12 m
D. 14 m
E. 25 m
Pahana
Ua ʻike ʻia:
Ka wikiwiki ma ke kuhikuhi ʻaoʻao (v_x) = 2 m/s
Ka wikiwiki ma ke kuhikuhi kū pololei (v_y) = 1,5 m/s
Ka manawa (t) = 4 kekona
Nīnau ʻia: Ka hoʻoneʻe ʻana o nā mea
Pane:
E helu i ka wikiwiki hopena o ka mea (v):

25. Nā Nīnau Hoʻokolohua Lahui 2007/2008 P4 Helu 3
Vector F₁ = 14 N a me F₂ = 10 Ua kau ʻia ʻo N ma kahi kiʻikuhi Cartesian e like me ka mea i hōʻike ʻia ma ke kiʻi. ʻO ka vector hopena inā i hōʻike ʻia ma nā vectors unit R = i + j ʻo ia….
A. 7i + 10√3 j
B. 7i + 10j
C. 3i + 7√3 j
D. 3i + 10j
E. 3i + 7j
Pahana
Ke helu nei i ka vector ʻāpana:
F_1x = (F₁)(cos 60^o) = (14)(0,5) = -7 N (hōʻailona maikaʻi ʻole no ka mea aia ia ma ke kuhikuhi x maikaʻi ʻole)
F_1y = (F₁)(hewa 60^o) = (14)(0,5√3) = 7√3 N (hōʻailona maikaʻi no ka mea aia ia ma ke kuhikuhi y maikaʻi)
F_2x = 10 N
F_2y = 0
Ke helu nei i ka vector ʻāpana hopena:
F_x =F_1x +F_2x +F_3x = -7 + 10 = 3 N
F_y =F_1y +F_2y +F_3y = 7√3 + 0 = 7√3 N
ʻO ka vector hopena inā i hōʻike ʻia ma nā vectors unit:
R = 3 i + 7√3 j
ʻO C ka pane pololei.

 

Puna nīnau:

Nā Nīnau Hoʻokolohua Lahui no ke Kino no ke Kula Kiʻekiʻe/Kula Kiʻekiʻe ʻOihana

Nā Nīnau Vector
1. ʻElua mau mana e kū pono ana kekahi i kekahi, ʻo ko lākou nui he 5 N a me 12 N. ʻO ka nui o ka hopena o nā mana ʻelua he … (Pane: 13 N)
2. Inā ʻo ka nui o ka vector B = 10 mau ʻāpana, hana ia i kahi kihi o 60^o me ka axis-x maikaʻi, a laila ʻo ka nui o ka vector ma ka axis-x a me ka axis-y he … (Pane: B_x = 5 , B_y = 5√3 )
3. ʻElua mau vectors ikaika F₁ a me F₂ ʻo kēlā me kēia he 3 N a me 4 N ka nui, he like ke kiko o ka pilina a ua hoʻopuni ʻia e kahi kihi o 60°, ʻo ka waiwai hopena o nā vectors ʻelua he... (Pane: F = √37 N)
4. ma₁ = 50 mau ʻāpana a me v₂ = 50 mau ʻāpana. Pehea ka nui o ka vector hopena?

(Pane: v = 50√2 mau ʻāpana)
5. Hele pololei kekahi keiki i 80 mika i ke kūkulu ʻākau, a laila huli i ka hikina no 80 mika, a huli hou i ka hema no 20 mika. ʻO ka neʻe ʻana o ke keiki mai ke kūlana mua mai….
(Pane: 100 mika, ma ka ʻākau hikina)
6. ʻO ka hopena o nā mana ʻekolu ma ke kiʻi ma lalo nei...
(Pane: 6 N)