12 mau laʻana o nā nīnau Vector Neʻe
1. Ua hana ʻo Fitria i kahi huakaʻi o ka hahai ʻana i kona mau kapuaʻi e hoʻomaka ana mai kahi A a i kahi B: 600 m ʻākau; a i kahi C 400 m komohana; a i kahi D 200 m hema; a laila e pau ana ma kahi E 700 m hikina. ʻO ka nui o ka neʻe ʻana i ʻike ʻia e Fitria….
A. 100 m
B. 300 m
C. 500 m
D. 1500 m
E. 1900 m
Pahana
Ua ʻike ʻia:
AF = AB – BF = AB – CD = 600 – 200 = 400 m EF = DE – DF = DE – BC = 700 – 400 = 300 m E hoʻohana i ke ʻano Pythagorean:
Hikina ʻĀkau.
ʻO C ka pane pololei.
2. Hele pololei kekahi keiki i 10 mika i ke komohana, a laila huli i ka hema no 12 mika, a huli hou i ka hikina no 15 mika. ʻO ka neʻe ʻana o ke keiki mai ke kūlana mua he...
A. 18 mika ma ke komohana hema
B. 14 mika hema
C. 13 mika hikina hema
D. 12 mika hikina
E. 10 mika hikina hema
3. Hele pololei kekahi keiki i 10 mika i ke komohana a laila huli i ka hema no 12 mika, a huli hou i ka hikina no 15 mika. ʻO ka neʻe ʻana o ke keiki mai ke kūlana mua he...
A. 18 mika ma ke komohana hema
B. 14 mika hema
C. 13 mika hikina hema
D. 12 mika hikina
E. 10 mika hikina hema
4. Hele pololei kekahi keiki i 1 mika i ke komohana, a laila huli i ka hema no 3 mika, a huli hou i ka hikina no 5 mika. ʻO ka neʻe ʻana o ke keiki mai ke kūlana mua he...
A. 18 mika ma ke komohana hema
B. 14 mika hema
C. 10 mika hikina hema
D. 6 mika hikina
E. 5 mika ma ka hikina hema
Pahana
5. Neʻe kekahi mea ma ke ala e like me ka mea i hōʻike ʻia ma ka pakuhi ma lalo nei:
ʻO ka neʻe ʻana i ʻike ʻia e kahi mea he….
A. 23 m
B. 21 m
C. 19 m
D. 17 m
E. 15 m
6. Holo kekahi keiki i 80 m i ke kūkulu ʻākau, a laila huli i 80 m i ka hikina a me 20 mika i ke kūkulu hema. ʻO ka nui o ka neʻe ʻana i hana ʻia e ke keiki he...
A. 060 m
B. 080 m
C. 100 m
D. 120 m
E. 180 m
7. 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
8. Neʻe kekahi mea i ka hikina he 40 m a laila i ka hikina ʻākau ma ke kihi o 37o i ka pae moe no 100 m a laila i ka ʻākau he 100 m. ʻO ka nui o ka neʻe ʻana i hana ʻia e ka mea…. (sin 37o = 0,6)
A. 180 m
B. 200 m
C. 220 m
D. 240 m
E. 300 m
Pahana
Ua ʻike ʻia:
Nīnau: Ka nui o ka neʻe ʻana (R)
Pane:
9. Neʻe kekahi mea he 4√3 m i ke komohana, a laila hoʻomau i kāna huakaʻi he 4 m i ke kūkulu ʻākau, a laila huli 60o i ka hikina no 8 m. ʻO ka nui o ka huakaʻi a ka mea i loaʻa he….
A. 2 m
B. 4 m
C. 4√3 m
D. 6 m
E. 8 m
Pahana
Ma muli o kēia helu ʻana, ua hoʻoholo ʻia ʻo ka waiwai o a = ka waiwai o a' = 4√3 mika.
E helu i ka neʻe ʻana o ka mea (R):
R = b' + d = 4 mika + 4 mika
R = 8 mika
ʻO ka pane pololei ʻo E.
10. Ma ka hanana "City Marathon Festival" ma ʻOkakopa 2014 ma Jakarta, he 4 mau māhele holo, ʻo ia hoʻi ka marathon piha (42 km), ka hapalua marathon (21 km), 10 kilomita, a me 5 kilomita, kahi i hoʻoholo ʻia ai ke ala no kēlā me kēia māhele. Ua hoʻomaka kēia heihei marathon mai ka hale ʻo Bung Karno Gelora a hoʻopau ma Monas. Ua komo kekahi o nā mea komo i kapa ʻia ʻo Andri i ka marathon piha a ua hiki iā ia ke uhi i ke ala mai nā kiko A, B, a me C e like me ka mea i hōʻike ʻia ma ke 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.
11. Neʻe kekahi mea i ka hikina 40 m a laila i ka hikina ʻākau ma ke kihi o 37 o i ka pae moe no 100 m a laila i ka ʻākau 100 m. ʻO ka nui o ka neʻe ʻana i hana ʻia e ka mea…. (sin 37 o = 0,6)
A. 180 m
B. 200 m
C. 220 m
D. 240 m
E. 300 m
Pahana
Ua ʻike ʻia:
a = 40 mika
b = ….
ʻo ke k = ….
d = 100 mika
e = 100 mika
θ = 37o
hewa 37o = 0,6
Nīnau: Ka nui o ka neʻe ʻana (R)
Pane:
E helu i ka waiwai o c:
Hewa 37o = c / d
0,6 = c / 100
c = (100)(0,6)
c = 60 mika
E helu i ka waiwai o b:
Hītū vector hopena ka hoʻoneʻe ʻana:
ʻO ka pane pololei ʻo B.
12. Neʻe kekahi mea he 4√3 m i ke komohana, a laila hoʻomau i kāna huakaʻi he 4 m i ke kūkulu ʻākau, a laila huli 60 o i ka hikina no 8 m. ʻO ka nui o ka huakaʻi a ka mea i loaʻa he….
A. 2 m
B. 4 m
C. 4√3 m
D. 6 m
E. 8 m
Pahana
Ua ʻike ʻia:
a = a' = 4√3 mika
b = b' = 4 mika
c = 8 mika
d = ……
Nīnau ʻia: Ka neʻe ʻana o ka mea (R)
Pane:
E helu i ka waiwai o d:
hewa 30o = d / c
0,5 = d / 8
d = (0,5)(8)
d = 4 mika
E helu i ka waiwai o a':
Ma muli o kēia helu ʻana, ua hoʻoholo ʻia ʻo ka waiwai o a = ka waiwai o a' = 4√3 mika.
E helu i ka neʻe ʻana o ka mea (R):
R = b' + d = 4 mika + 4 mika
R = 8 mika
ʻO ka pane pololei ʻo E.
Puna nīnau:
Nā Nīnau Hoʻokolohua Lahui no ke Kino no ke Kula Kiʻekiʻe/Kula Kiʻekiʻe ʻOihana
