He tauira pātai hei whakatau i te wā o te nekehanga parabolic

4 ngā tauira pātai mō te whakatau i te wā o te nekehanga parabolic

1. Ka whanahia te pōro ki runga i te koki o te 30^o ki te mata o te papa me te tere tīmatanga o te 10 m/s. Tātaihia te wā e eke ai te pōro ki tōna teitei mōrahi! Te whakaterenga o te kaha ā-papa = 10m/s²
Kōrero
E mōhiotia ana:
Koki (θ) = 30^o
Te tere tīmatanga (v)_o) = 10 m/s
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s²
I pātaihia: Te wā e eke ai te pōro ki tōna teitei mōrahi
Whakautu:
Te tere tīmatanga o te pōro i te ahunga poutū:
v_oy = v_o sin θ = (10 m/s)(sin 30^o) = (10 m/s)(0,5) = 5 m/s

Ka tatauhia te wā e eke ai te pōro ki tōna teitei mōrahi mā te whakamahi i te tātai nekehanga poutū ki runga.
I roto i te whakaoti rapanga e pā ana ki te nekehanga poutū ki runga, ka hoatu he tohu pai ki te rahinga whārite e anga ana ki runga, rahinga wetere ka hoatu he tohu kino ki te ahunga whakararo.
E mōhiotia ana:
Te tere tīmatanga (v_o) = 5 m/s (he pai nā te mea kei runga te ahunga o te tere tīmatanga)
Te whakaterenga nā te kaha ā-papa (g) = -10 m/s² (kino nā te mea kei raro te ahunga o te whakaterenga ā-papa)
Te tere whakamutunga (v_t) = 0 (i te teitei mōrahi, ka noho pūmau te mea mō tētahi wā poto i mua i te huri i te ahunga)
I pātaihia: Wā wā (t)
Whakautu:
E mōhiotia ana ko v_o, g me v_t, i pātaihia a t, nō reira ka whakamahia te tātai v_t = v_o + gt
v_t = v_o + gt
0 = 5 + (-10)t
0 = 5 – 10 t
5 = 10 tāra
t = 5/10 = 0,5 hēkona
Ko te wā e eke ai te pōro ki tōna teitei mōrahi he 0,5 hēkona.

2. Ka whiua te pōro ki runga i te koki o te 30^o he poutū me te tere tīmatanga o te 8 m/s. Kia pēhea te roa ka tae atu te pōro kinekehanga parabolic! Te whakaterenga nā te kaha ā-papatipu = 10 m/s²
Kōrero
E mōhiotia ana:
Koki (θ) = 30^o
Te tere tīmatanga (v_o) = 8 m/s
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s²
I pātaihia: Te wā e neke ai te pōro i roto i te parabola
Whakautu:
Te tere tīmatanga o te pōro i te ahunga poutū:
v_oy = v_o sin θ = (8 m/s)(sin 30^o) = (8 m/s)(0,5) = 4 m/s

Tuatahi, tatauhia te wā e eke ai te mea ki tōna teitei mōrahi mā te whakamahi i te tātai mō te nekehanga poutū ki runga.
I te whakaoti rapanga mō te nekehanga poutū ki runga, ka hoatu he tohu pai ki te rahinga whārite e anga ana ki runga, ka hoatu he tohu kino ki te rahinga whārite e anga ana ki raro.
E mōhiotia ana:
Te tere tīmatanga (v_o) = 4 m/s (he pai nā te mea kei runga te ahunga o te tere tīmatanga)
Te whakaterenga nā te kaha ā-papa (g) = -10 m/s² (kino nā te mea kei raro te ahunga o te whakaterenga ā-papa)
Te tere whakamutunga (v_t) = 0 (i te teitei mōrahi, ka noho pūmau te mea mō tētahi wā poto i mua i te huri i te ahunga)
I pātaihia: Wā wā (t)
Whakautu:
E mōhiotia ana ko v_o, g me v_t, i pātaihia a t kia whakamahia ai te tātai v_t = v_o + gt
v_t = v_o + gt
0 = 4 + (-10)t
0 = 4 – 10 t
4 = 10 tāra
t = 4/10 = 0,4 hēkona
Ko te wā e eke ai te pōro ki tōna teitei mōrahi he 0,4 hēkona.
He ōrite te ara o te pōro, nō reira ko te wā e neke ake ai te pōro he rite tonu ki te wā e neke iho ai te pōro. Nō reira, ko te wā katoa he 2 x 0,4 hēkona = 0,8 hēkona.

3. Ka pupuhihia te matā ki runga i te koki o te 30°^o whakapae mai i tētahi pūwāhi 10 mita i runga ake i te whenua. Ko te tere tīmatanga o te matā he 40 m/s. Kia pēhea te roa ka tae te matā ki te whenua? Ko te whakaterenga nā te kaha ā-papatipu he 10 m/s²
Kōrero
E mōhiotia ana:
Koki (θ) = 30^o
Teitei tīmatanga (h_o) = 10 mita
Te tere tīmatanga (v_o) = 40 m/s
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s²
I pātaihia: Te wā e rere ana te matā i te rangi
Whakautu:
Te tere tīmatanga o te pōro i te ahunga poutū:
v_oy = v_o sin θ = (40 m/s)(sin 30^o) = (40 m/s)(0,5) = 20 m/s

Tuatahi, tatauhia te wā e eke ai te matā ki tōna teitei mōrahi mā te whakamahi i te tātai mō te nekehanga poutū ki runga.
I te whakaoti rapanga mō te nekehanga poutū ki runga, ka hoatu he tohu pai ki te rahinga whārite e anga ana ki runga, ka hoatu he tohu kino ki te rahinga whārite e anga ana ki raro.
E mōhiotia ana:
Te tere tīmatanga (v_o) = 20 m/s (he pai nā te mea kei runga te ahunga o te tere tīmatanga)
Te whakaterenga nā te kaha ā-papa (g) = -10 m/s² (kino nā te mea kei raro te ahunga o te whakaterenga ā-papa)
Te tere whakamutunga (v_t) = 0 (i te teitei mōrahi, ka noho pūmau te mea mō tētahi wā poto i mua i te huri i te ahunga)
I pātaihia: Wā wā (t)
Whakautu:
E mōhiotia ana ko v_o, g me v_t, i pātaihia a t kia whakamahia ai te tātai v_t = v_o + gt
v_t = v_o + gt
0 = 20 + (-10)t
0 = 20 – 10 t
20 = 10 tāra
t = 20/10 = 2 hēkona
Ko te wā e eke ai te pōro ki tōna teitei mōrahi he 2 hēkona.
He ōrite te ara o te pōro, nō reira ko te wā e rere ana te pōro i te rangi he 2 x 2 hēkona = 4 hēkona.

Ka pupuhihia he matā mai i tētahi pūwāhi e 10 mita te teitei i runga ake i te whenua. E 4 hēkona te roa ka tae te pōro ki tōna pūwāhi tīmatanga. Ka haere tonu te pōro ki raro.

Ka tatauhia te wā e neke ai te pōro mai i te teitei o te 10 mita hei whakatau i te wā mō te nekehanga taka noa.
E mōhiotia ana:
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s²
Teitei (h) = 10 mita
I pātaihia: Wā wā (t)
Whakautu:
I hoatu a g, h, ā, i tonoa a t kia rite ai te tātai nekehanga hinga noa i whakamahia h = 1/2 gt²
h = 1/2 gt²
10 = 1/2 (10) t²
10 = 5 tāra²
t² = 10/5 = 2
t = √2 = 1,4 hēkona
Ko te wā e taka ai te matā mai i te teitei o te 10 mita he 1,4 hēkona.

Ko te roanga katoa o te wā e rere ana te matā i te rangi he 4 hēkona + 1,4 hēkona = 5,4 hēkona.

4. Ka whiua whakararatia tētahi māpere ki te taha matau mai i te teitei o te 5 mita me te tere tīmatanga o te 15 m/s. Tātaihia te wā e noho ana te māpere i te rangi! Te whakaterenga nā te kaha ā-papatipu = 10 m/s²
Kōrero
E mōhiotia ana:
Teitei (h) = 5 mita
Te tere tīmatanga (v_o) = 15 m/s
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s²
I pātaihia: Te wā e rere ana te māpere i te rangi
Whakautu:
Ko te ara o te māpere e whakaaturia ana i te pikitia. Ka tatauhia te wā e noho ana te māpere i te rangi mā te whakamahi i te tātai nekehanga hinga noa.
E mōhiotia ana:
Teitei (h) = 5 mita
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s²

I pātaihia: Wā wā (t)
Whakautu:
I hoatu a g, h, ā, i tonoa a t kia rite ai te tātai nekehanga hinga noa i whakamahia h = 1/2 gt²
h = 1/2 gt²
5 = 1/2 (10) t²
5 = 5 tāra²
t² = 5/5 = 1
t = √1 = 1 hēkona
Ko te wā e taka ai te matā mai i te teitei o te 5 mita he 1 hēkona.

[Reo Pākehā: Te whakaoti rapanga nekehanga pere – te whakatau i te wā ]