Wetereo – ngā raruraru me ngā otinga
Te Wetereo me te Tauine
1. I roto i ngā kōwhiringa e whai ake nei, ko ngā takirua tauine-tauine…
A. Te kaha – te whakaterenga
B. Pēhanga – kaha
C. Te nekehanga – tere
D. Iahiko – pēhanga
Rongoā:
Te kaha = te whārite, te whakaterenga = te whārite
Pēhanga = tauine, kaha = whārite
Nekehanga = te whārite, te tere = te tauine
Iahiko = tauine, pēhanga = tauine
Ko te whakautu tika ko B.
2.
Ko te whakautu tika e whakaaturia ana e te tau…
A. 1 me te 4
B. 1 me te 2
C. 2 me te 3
D. 3 me te 4
Rongoā:
Tere = tauine
Nekehanga = whārite
Taumaha = whārite
Whakaterenga = whāka
Ko te whakautu tika ko C.
Ngā wāhanga o ngā whārite
3. E rua ngā whārite, F 1 = 20 N me F 2 = 30 N, ko te ahunga kei a rāua e whakaaturia ana i te pikitia i raro nei. Tātaihia te hua o ngā wāhanga o ngā whārite i te tuaka-x me te tuaka-y.
A. 5√3 N me te -25 N
B. -5√3 N me te 25 N
C. 25 N me te 5√3 N
D. 30 N me 25√3 N
Mōhiotia:
F 1 = 20 Newton
Koki i waenganui i te tuaka F 1 me te tuaka x = 30 o
F 2 = 30 Newton
Koki i waenganui i te tuaka F 2 me te tuaka x =30 o
E hiahiatia ana: F x me F y
Rongoā:
F 1x = F 1 cos 30 o = (20)(0.5√3) = 10√3 Newton (tohu tāpiri nā te mea e tohu ana ki te tuaka +x)
F 1y = F 1 sin 30 o = (20)(0.5) = 10 Newton (tohu tāpiri nā te mea e tohu ana ki te tuaka +y)
F 2x = F 2 cos 30 o = (30)(0.5√3) = -15√3 Newton (tohu tango nā te mea e tohu ana ki te tuaka -x)
F 2y = F 2 sin 30 o = (30)(0.5) = 15 Newton (tohu tāpiri nā te mea e tohu ana ki te tuaka +y)
Ko te hua o te wāhanga x:
F x = F 1x + F 2x = 10√3 N – 15√3 N = -5√3 Ngā Newton
Ko te hua o te wāhanga y:
Fy = F 1y + F 2y = 10 N + 15 N = 25 Ngā Newton
Ko te whakautu tika ko B.
Ko te hua o ngā whārite e rua
4. Tokorua ngā tamariki a A rāua ko B e pana ana i tētahi poraka, ki te panaia e A te poraka ki te tonga me te kaha o te 400 N, ā, i taua wā anō ka panaia e B te poraka ki te rawhiti me te kaha o te 300 N, kātahi ka whakatau i te hua o te kaha A me B.
A. 100 N whaka te tonga
B. 100 N ki te rawhiti
C. 500 N ki te tonga-mā-rāwhiti
D. 700 N ki te tonga-mā-rāwhiti
Mōhiotia:
U = raki, T = rawhiti, S = tonga, B = hauauru
TL = mā rāwhiti, TG = tonga-mā-rāwhiti, BD = tonga-mā-uru, BL = mā uru-mā-uru
A = 400 Newton ki te tonga
B = 300 Newton ki te rawhiti
E hiahiatia ana: te rahi me te ahunga o te kaha kupenga (R)
Rongoā:
Ko te whakautu tika ko C.
Ko te hua o te wetere o te nekehanga
5. E eke motopaika ana tetahi mai i te kāinga, 6 kiromita ki te raki, kātahi ka 8 kiromita ki te rawhiti. Tāutuhia te tūranga whakamutunga o te tangata mai i te tūranga tīmatanga.
A. 14 kiromita ki te raki-mā-rāwhiti
B. 14 kiromita ki te tonga mā uru
C. 10 kiromita ki te raki-mā-rāwhiti
D. 10 kiromita ki te raki mā uru
Mōhiotia:
E hiahiatia ana: te rahi me te ahunga o te nekehanga hua
Rongoā:
Ko te whakautu tika ko C.
6.
E ai ki te pikitia i runga ake nei, mēnā ko te 1 tapawhā te tohu mō te 1 km, he aha te nekehanga katoa?
Rongoā:
Tawhiti = A + B + C = 6 + 6 + 2 = 14 kiromita
Nekehanga = R = 12 km
7. Ka haere tētahi motuka mai i A ki B i te 30 km ki te raki, kātahi ka 60 km ki te rawhiti, kātahi ka 110 km ki te tonga. Tātaihia te nekehanga o te motuka mai i A ki D.
Rongoā:
AA' = 60 kiromita
A'D = 110 km – 30 km = 80 km
8. Ka haere tētahi motuka mai i te tāone A ki te tāone B 100 km ki te raki, kātahi ki te tāone C 60 km ki te rawhiti, kātahi ki te tāone D 20 km ki te tonga. Tātaihia te nekehanga o te motuka.
Rongoā:
D'D = 60 kiromita
AD' = 100 km – 20 km = 80 km
- He aha te wetereo?
- whakahoki: He rahinga te whārite, ā, he ahunga anō hoki tōna. Ko ētahi tauira ko te tere, te kaha, me te whakaterenga.
- He aha te rerekētanga o te wetereo mai i te tauine?
- whakahoki: He rahi anake te rahi o te tauine, engari he rahi me te ahunga o te whārite. Hei tauira, he taurite te pāmahana nā te mea he uara engari kāore he ahunga, engari he whārite te tere nā te mea e tohu ana i te tere (rahi) i tētahi ahunga.
- Me pēhea te whakaatu i tētahi wetereo mā te whakairoiro?
- whakahoki: Ka taea te whakaatu i tētahi whārite mā te pere. Ko te roa o te pere e tohu ana i te rahi o te whārite, ā, ko te ahunga o te pere e tohu ana i te ahunga o te whārite.
- He aha te hiranga o te hiku me te pane o tētahi whārite?
- whakahoki: Ko te hiku te tīmatanga o te whārite, ā, ko te pane (te pito rānei) te mutunga. Ina mahihia ngā mahi pēnei i te tāpiri whārite, ka whakanohoia te hiku o tētahi whārite ki te pane o tētahi atu.
- Me pēhea te tāpiri i ngā wetereo?
- whakahoki: Ka tāpirihia ngā whārite mā te whakamahi i te tikanga pane-ki-te-hiku. Ka whakatakotoria te hiku o te whārite tuarua ki te pane o te tuatahi. Kātahi ka tangohia te whārite hua mai i te hiku o te whārite tuatahi ki te pane o te whārite tuarua.
- He aha te rerekētanga i waenga i te wekere kotahi me te wekere kore?
- whakahoki: Kotahi te rahi o te whārite kotahi, ā, e tohu ana i tētahi ahunga kua tohua. Ka whakamahia hei tohu i te ahunga o tētahi whārite, ahakoa tōna rahi. Kāore he rahi, kāore hoki he ahunga motuhake o te whārite kore (kore rānei).
- Me pēhea te whakarea i tētahi whārite ki tētahi tauine?
- whakahoki: Mā te whakarea i tētahi irahiko ki tētahi tauine ka rerekē tōna rahi engari kāore tōna ahunga. Mena he pai te tauine, ka noho tonu te ahunga; ki te kino, ka hurihia te ahunga.
- He aha te tikanga o te mea he poutū, he poutū rānei ngā whārite e rua?
- whakahoki: He poutū, he āwhata rānei ngā whārite e rua mēnā he 90 nekehanga te koki i waenganui i a rāua. Ka kore te hua ira.
- Me pēhea te whakatau i te hua o ngā pūwero e rua?
- whakahoki: Ko te hua ko te tapeke o ngā whārite e rua. Ina whakaatuhia ngā whārite hei pere, ka kitea te hua mā te whakanoho i te hiku o te whārite tuarua ki te pane o te tuatahi, ka tuhia he pere hou (te hua) mai i te hiku o te whārite tuatahi ki te pane o te tuarua.
- Mena ka anga whaka te rawhiti o tētahi whēkere me te rahi o te 10 waeine, me pēhea e whakaahua ai i tōna ritenga kē?
- whakahoki: Ko te ahunga ritenga kē o tēnei whārite he rite tonu te rahi (10 ngā waeine) engari ka tohu ki te ahunga ritenga kē, arā, ki te hauauru.
