Te nekehanga poutū – ngā raruraru me ngā otinga
1. Ka whiua poutū ake a Pōro A me te tere o te 10 m/s. I muri i te 1 hēkona, mai i taua tūranga anō, ka whiua poutū ake a Pōro B i te ara kotahi, me te tere o te 25 m/s. He aha te teitei o te pōro B ina tūtaki ki a Pōro A?
Rongoā:
I te whakaoti rapanga o te nekehanga poutū , ka hoatu he tohu pai ki te rahinga whārite e anga whakarunga ana, ka hoatu he tohu kino ki te rahinga whārite e anga whakararo ana.
Mōhiotia:
Te tere tīmatanga (v o ) o te pōro A = 10 m/s
Te wā (t) o te pōro A = x
Te tere tīmatanga (v o ) o te pōro B = 25 m/s
Te wā (t) o te pōro B = x – 1
Te whakaterenga nā te kaha ā-papatipu (g) = -10 m/s 2 (ka hoatu te tohu tango nā te mea kei raro te ahunga o te kaha ā-papatipu )
E hiahiatia ana: Te teitei o te pōro B ina tūtaki ki te pōro A (h)
h A = h B
hua + ½ gt 2 = hua + ½ gt 2
10x + ½ (-10) x 2 = 25 (x-1) + ½ (-10) (x-1) 2
10x – 5x 2 = 25 (x-1) – 5 (x-1) 2
10x – 5x 2 = 25x – 25 – 5 (x 2 -2x+1)
10x – 5x 2 = 25x – 25 – 5x 2 + 10x – 5
10x – 5x 2 – 25x + 25 + 5x 2 – 10x + 5 = 0
– 5x 2 + 5x 2 + 10x – 25x – 10x + 25 + 5 = 0
10x – 25x – 10x + 25 + 5 = 0
– 25x + 25 + 5 = 0
– 25x + 30 = 0
– 25x = – 30
x = -30/-25
x = 1.2 hēkona
Te wā i waenganui i te pōro A i te rangi i mua i tōna tūtakitanga ki te pōro B = 1.2 hēkona
Ko te wā i noho ai te pōro B i te rangi i mua i tōna tūtakitanga ki te pōro A = 1.2 hēkona – 1 hēkona = 0.2 hēkona.
Ko te teitei o te pōro A ina tūtaki ki te pōro B:
h = v o t + ½ gt 2 = (10)(1.2) + 1/2 (-10)(1.2) 2 = 12 – 5(1.44) = 12 – 7.2 = 4.8 mita s
Ko te teitei o te pōro B ina tūtaki ki te pōro A:
h = v o t + ½ gt 2 = (25)(0.2) + 1/2 (-10)(0.2) 2 = 5 – 5(0.04) = 5 – 0.2 = 4.8 mita s
1. Pātai: He aha te tikanga o te nekehanga poutū?
Whakautu: Ko te nekehanga poutū e pā ana ki te nekehanga o tētahi mea ki runga, ki raro rānei, i raro i te mana o te kaha ā-papa.
2. Pātai: He aha te hiranga o te whakaterenga nā te kaha ā-papa (g) i roto i te nekehanga poutū?
Whakautu: Ka pāngia ngā mea katoa e tata ana ki te mata o Papatūānuku e te whakaterenga pumau, , arā, tata ki te 9.81 m/s² ki raro.
3. Pātai: Ka taea e te mea te whai tere tīmatanga i roto i te nekehanga poutū?
Whakautu: Ae, ka taea e ngā mea te whai tere tīmatanga ki runga, ki raro rānei ina tīmata tā rātou nekehanga poutū.
4. Pātai: He aha te mea ka pā ki te tere o te taka noa o tētahi mea?
Whakautu: Ka piki ake te tere o tētahi mea e hinga noa ana mā te 9.81 m/s ia hekona nā te kaha o te kaha ā-papa.
5. Pātai: He aha te hononga o te wā piki ki te wā heke mō tētahi mea e whiua poutū ana?
Whakautu: Mō tētahi mea e whiua ana ki runga, kātahi ka tukua kia taka whakamuri, ko te wā piki ka rite ki te wā heke.
6. Pātai: He aha te tere o tētahi mea i tōna teitei rawa?
Whakautu: I te teitei rawa, ka kore te tere poutū o te mea i mua i tōna tīmatanga ki te heke.
8. Pātai: He aha te pānga o te ātete hau ki te nekehanga poutū?
Whakautu: Ka ārai te ātete hau i te nekehanga, ka whakaiti i te whakaterenga me te tere mutunga mō ngā mea e hinga ana.
9. Pātai: He aha te tere whakamutunga?
Whakautu: Ko te tere whakamutunga ko te tere mōrahi pumau e taea ana e tetahi mea e hinga ana ina rite te ātete o te hau ki te kaha o te papatipu.
10. Pātai: Ka taea e te mea te whakaterenga kino i te wā e neke ana ki runga?
Whakautu: Ae, ina neke ake tetahi mea ki te ātete ki te kaha ā-papatipu, he rite te whakaterenga kino ki te -g.
12. Pātai: He aha i kino ai te whakaterenga mō ngā mea e whiua ana ki runga?
Whakautu: Nā te mea ka heke te whakaterenga nā te kaha ā-papa, ka kiia he kino mō ngā mea e neke ana i te huarahi whakamuri.
14. Pātai: He aha te hinganga kore utu?
Whakautu: Ko te hinganga noa te nekehanga o tētahi mea i raro i te awe o te kaha ā-papa, kāore he kaha kē atu e pā ana ki taua mea.
15. Pātai: He aha te rerekētanga o te nekehanga o tētahi mea ina makahia ki raro, ki te nekehanga rānei ina tukua?
Whakautu: Ka pāngia rāua e te whakaterenga ā-papatipu. Heoi, he tere tīmatanga tāpiri tō te mea e whiua ana ki raro, ā, ka tere ake tōna taenga ki te whenua i te mea e tukua noa ana.
16. Pātai: He aha ngā āhuatanga e pā ana ki te tere whakamutunga o tētahi mea?
Whakautu: Kei roto i ngā āhuatanga te papatipu o te mea, te āhua, te horahanga o te mata, me te kiato me te matotoru o te rauemi e taka ana mā roto.
17. Pātai: He pūngao nekeneke me te pūngao pūmanawa tō te mea e neke poutū ana?
Whakautu: Ae, ka piki te kaha nekeneke o te mea i a ia e hinga ana, ka heke tōna kaha pūmanawa, ā, ka pērā anō i te pikinga.
18. Pātai: He aha i rerekē ai te tere o te mea i te wā e neke poutū ana?
Whakautu: Ka puta he whakaterenga pumau i te kaha ā-papa, ka whakarerekē i te tere o te mea kia tae rā anō ki te tere whakamutunga, kia huri rānei te ahunga.
19. Pātai: Ka taea te whakaahua i te nekehanga poutū hei nekehanga tere ōrite?
Whakautu: Ae, i te korenga o te ātete hau, ka tere ōrite te nekehanga poutū i raro i te kaha ā-papa me te tere o te .
20. Pātai: Me pēhea te whakamahi i te mātāpono tiaki pūngao ki te nekehanga poutū?
Whakautu: Ka noho pūmau tonu te tapeke o te pūngao nekeneke me te pūngao pūmanawa i te nekehanga poutū, me te whakaaro kāore he ngaronga pūngao nā te ātete hau.
He mea nui te mārama ki te nekehanga poutū i roto i te hangarau matarohia, ā, he maha ngā tono whai hua mai i te pūtaiao hākinakina ki ngā ture hangarau me te haumaru.
