Te nekehanga hinga noa – ngā raruraru me ngā otinga
1. Ka taka noa tetahi kōhatu mai i te teitei o te 45 mita. Mena ko te whakaterenga nā te kaha ā-papa he 10 ms -2 , he aha te tere o te kōhatu ina pā ki te whenua?
Mōhiotia:
Teitei (h) = 45 mita
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
E hiahiatia ana: Te tere whakamutunga o te kōhatu ina pā ki te whenua ( vt )
Rongoā:
Te whārite o te nekehanga taka noa :
v t 2 = 2 gh
Te tere whakamutunga o te kōhatu:
v t 2 = 2 (10)(45) = 900
v t = √900 = 30 m/s 2
2. Ka taka noa tetahi mea mai i te teitei, kāore he tere tīmatanga. Ka pā te mea ki te whenua i muri i te 2 hēkona. Ko te whakaterenga nā te kaha ā-papa he 10 ms -2 . Tātaihia te teitei.
Mōhiotia:
Wā wā (t) = 2 hēkona
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Teitei e hiahiatia ana: Teitei (h)
Rongoā:
Ko te whārite o te nekehanga hinga noa:
h = ½ gt 2
Te teitei:
h = ½ (10)(2) 2 = (5)(4) = 20 mita
3. He taka noa te mea 2-kg mai i te teitei o te 20 mita i runga ake i te whenua. He aha te wā i waenganui i te mea i te rangi? Ko te tere o te kaha ā-papa he 10 ms -2
Mōhiotia:
Teitei (h) = 20 mita
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
E hiahiatia ana : Te wā (t)
Rongoā:
Te whārite o te nekehanga hinga noa:
h = ½ gt 2
Wā ā-wā:
20 = ½ (10)(t 2 )
20 = (5)(t 2 )
20/5 = t 2
4 = t 2
t = √4
t = 2 hēkona
4. E rua ngā mea, te mea 1 me te mea 2, e taka noa ana mai i te teitei o h 1 me h 2 i te wā kotahi. Mēnā ko h 1 : h 2 = 2 : 1, he aha te ōwehenga o te wā mai i te mea 1 ki te mea 2?
Mōhiotia:
Ko te teitei o te mea 1 (h 1 ) = 2
Ko te teitei o te mea 2 (h 2 ) = 1
Te whakaterenga nā te kaha ā-papatipu = g
E hiahiatia ana: t 1 : t 2
Rongoā:
Ahanoa 1:
h 1 = 1/2 gt 1 2
2 = 1/2 = 1 2
(2)(2) = gt 1 2
4 = gt 1 2
4/g = t 1 2
t 1 = √4/g
Ahanoa 2:
h 2 = 1/2 gt 2 2
1 = 1/2 = 2 2
(2)(1) = gt 2 2
2 = gt 2 2
2/g = t 2 2
t 2 = √2/g
Te ōwehenga o ngā wā:
t 1 : t 2
√4/g : √2/g
(√4/g) 2 : (√2/g) 2
4/g: 2/g
4: 2
2: 1
5. He mea i taka iho i te teitei o te h i runga ake i te whenua. Ko te tere whakamutunga ina pā te mea ki te whenua ko te 10 m/s. He aha te wā e toe ana hei tae atu ki te ½ h i runga ake i te whenua? Ko te whakaterenga nā te kaha ā-papatipu ko te 10 m/ s2.
Mōhiotia:
Ko te tere whakamutunga (v t ) = 10 m/s
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
E hiahiatia ana: Te wā e tae atu ai ki te 1/2 hāora i runga ake i te whenua
Rongoā:
Te teitei o te h:
v t 2 = 2 gh
10 2 = 2 (10) hāora
100 = 20 hāora
h = 100 / 20
h = 5 mita
Ko te teitei o te 1/2 h = 1/2 (5 mita) = 2.5 mita. Ko te wā e hiahiatia ana hei eke ki te 2.5 mita i runga ake i te whenua:
h = 1/2 gt 2
2.5 = 1/2 (10) t 2
2.5 = 5 t 2
t 2 = 2.5 / 5 = 0.5 = (0.25)(2)
t = √(0.25)(2) = 0.5√2 = 1/2 √2 hēkona
6.
Ko te nekehanga hinga noa o te kokonati ( pikitia 1 ) me te nekehanga o te pōro i whiua poutū ki runga ki te pūwāhi teitei rawa atu e te ākonga (pikitia e 2). Whakatauhia te momo o ngā nekehanga e rua.
Rongoā:
Pikitia 1 = nekehanga hinga noa = Whakaterenga
Pikitia 2 = nekehanga poutū = Whakaroa
Ko te whakautu tika ko A.
7. Ka taka noa te kōhatu i tētahi whare. Ko te wā e hiahiatia ana e te kōhatu kia tae ki te whenua he 3 hēkona, ā, ko te whakaterenga nā te kaha ā-papa he 10 m/s2 . Tātaihia te teitei o te whare.
A. 15 mita
B. 20 mita
C. 30 mita
D. 45 mita
Mōhiotia:
Wā wā (t) = 3 hēkona
Te whakaterenga nā te kaha ā-papa (g) = 10 ms -2
E hiahiatia ana: Teitei o te whare (h)
Rongoā:
E mōhiotia ana: te wā (t) me te whakaterenga nā te kaha ā-papa (g), e hiahiatia ana: te teitei (h) nō reira whakamahia te whārite o te nekehanga taka noa: h = ½ gt 2
h = ½ (10)(3)
h = (5)(3)
h = 15 mita
Ko te whakautu tika ko A.
8. Ka taka noa tetahi hua i tōna rākau i te teitei o te 12 m i runga ake i te whenua. Mena ko te whakaterenga nā te kaha ā-papa he g = 10 m/s 2 , ā, kāore e arohia te waku o te hau, tātaihia te teitei o te hua i runga ake i te whenua i muri i te 1 hēkona.
A. 7 mita
B. 6 mita
C. 5 mita
D. 4 mita
Mōhiotia:
Teitei o te rākau (h) = 12 mita
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Wā wā (t) = 1 hēkona
E hiahiatia ana: Te teitei o te hua i runga ake i te whenua
Rongoā:
I muri i te 1 hēkona, ka taka noa te hua ki:
h = ½ gt 2 = ½ (10)(1) 2 = (5)(1) = 5 mita
Te teitei o te hua i runga ake i te whenua i muri i te 1 hēkona:
12 mita – 5 mita = 7 mita
Ko te whakautu tika ko A.
- He aha te nekehanga taka noa?
Whakautu : Ko te nekehanga taka noa e pā ana ki te nekehanga o tētahi mea i raro i te mana o te kaha ā-papa anake, kāore he kaha kē atu (pēnei i te ātete hau) e pā ana ki taua mea.
- He pēhea te tere o te kaha ā-papa, e whakaatuhia ana i te nuinga o te wā hei , ka pā ki tētahi mea e hinga noa ana?
Whakautu : Ko ngā mea katoa e taka noa ana i te mata o te Ao ka pāngia e te whakaterenga pumau nā te kaha ā-papa, , e tata ana ki ki raro. Ko te tikanga tēnei ka piki ake te tere o te mea mā tēnei nui mō ia hēkona o te taka noa.
- Mena he iti noa te ātete o te hau, ka pēhea te awe o te papatipu o tētahi mea ki tōna whakaterenga hinga kore utu?
Whakautu : I te korenga o te ātete hau, kāore te papatipu o tētahi mea e pā ki tōna whakaterenga hinga noa. Ka hinga ngā mea katoa, ahakoa te papatipu, me te whakaterenga ōrite nā te kaha ā-papa, .
- He aha te āhua o ngā kairangi moana e mānu ana i roto i te Teihana Wāhi Ātea o te Ao (ISS) mēnā kei reira tonu te kaha ā-papa?
Whakautu : Te āhua nei kei te mānu ngā kairangi aorangi i roto i te ISS, ehara i te mea nā te korenga o te kaha ā-papa, engari nā te mea kei roto tonu ngā kairangi aorangi me te ISS i te āhua taka noa huri noa i te Ao. Kei te taka tonu rātou i te tere ōrite ki te ISS, ka puta he ahua kore taumaha.
- He aha te rerekētanga i waenga i te taumaha me te papatipu i roto i te horopaki o te hinganga kore utu?
Whakautu : Ko te papatipu he ine i te nui o te matū i roto i tētahi mea, ā, ka noho pūmau ahakoa tōna taunga. Ko te taumaha, i tētahi atu ringa, ko te kaha e pā ana ki tētahi mea nā te kaha ā-papatipu. Ka rerekē i runga i te papa ā-papatipu. I te wā e hinga noa ana, ka ahua kore taumaha te mea nā te mea kāore he kaha noa e pā ana ki a ia, engari ka noho tonu tōna papatipu.
- Ki te whiua ake tētahi mea ki runga, ka pēhea tōna tere i a ia e piki ana? Ā, ka pēhea hoki ina tīmata te taka ki raro?
Whakautu : Ina whiua ki runga tētahi mea, ka heke te tere i raro i te mana o te kaha ā-papa. Ka heke tōna tere tae noa ki te kore i tōna taumata teitei rawa. I a ia e tīmata ana ki te hinga ki raro, ka tere ake nā te kaha ā-papa, ka piki ake tōna tere ki raro.
- He aha te tere whakamutunga i roto i te horopaki o te hinganga kore utu?
Whakautu : Ko te tere whakamutunga ko te tere mōrahi pumau e taea ana e te mea e hinga ana ina taurite te kaha o te kaha ā-papa ki raro me te kaha o te ātete hau ki runga. I tēnei wā, kāore te mea e tere haere ana, ā, ka hinga tonu i te tere pumau.
- He pēhea te pānga o te teitei e taka iho ana tētahi mea ki te wā e pau ana ki te tau ki te whenua?
Whakautu : Ko te wā e pau ana ki te taunga o tētahi mea ki te whenua he rite ki te pūtake tapawhā o te teitei e taka iho ana (ki te kore he ātete hau). Ka roa ake te taunga o tētahi mea i taka iho i tētahi teitei nui atu i tētahi i taka iho i tētahi teitei poto ake.
- He aha te mea ka pā ki te pūngao pūmanawa o tētahi mea ina taka noa i raro i te kaha ā-papa?
Whakautu : I te taka noa o te mea i raro i te kaha ā-papa, ka heke tōna kaha pūmanawa (e pā ana ki te whenua). Ka hurihia tēnei hekenga o te kaha pūmanawa hei kaha nekeneke, ka piki ake te tere o te mea.
- Ki te takahia ētahi mea e rua, he rerekē te āhua engari he ōrite te papatipu, mai i te teitei kotahi i roto i te korehau, ko tēhea te mea ka pā tuatahi ki te whenua?
Whakautu : I roto i te korehau, ki te kore he ātete hau, ka pā ngā mea e rua ki te whenua i te wā kotahi. Kāore he aha o rāua āhua nā te mea ko te kaha ā-papa anake e pā ana ki a rāua, ā, he ōrite ō rāua taumaha.
