ahupūngao

1. Ka wehe atu te whutupōro i te whenua i te koki θ = 30^o ki te whakapae me te tere tīmatanga o te 14 m/s. Tātaihia te tere whakamutunga i mua i te pānga o te pōro ki te whenua.

Mōhiotia:

Koki (θ) = 30^o

Te tere tīmatanga (v_o) = 14 m/s

Te whakaterenga o te kaha ā-papa (g) = 10 m / s²

E hiahiatia ana: Te tere whakamutunga i mua i te pa o te pōro ki te whenua

Rongoā:

Wāhanga whakapae o te tere tīmatanga:

v_ox = v_o cos θ = (14 m/s)(cos 30^o) = (14 m/s)(0.5√3) = 7√3 m / s

Wāhanga poutū o te tere tīmatanga:

v_oy = v_o sin θ = (14 m/s)(sin 30^o) = (14 m/s)(0.5) = 7 m/s

Te tere whakamutunga i te ahunga poutū

Kōwhiria te ahunga whakarunga hei pai, me te ahunga whakararo hei kino.

Mōhiotia:

Te tere tīmatanga (v_o) = 7 m/s (pai ki runga)

Te whakaterenga o te kaha ā-papa (g) = –10 m / s² (kino ki raro)

Teitei (h) = 0 (hoki te mea ki tōna tūranga tīmatanga)

E hiahiatia ana: Te tere whakamutunga (v_t)

Rongoā:

v_t² = v_o² + 2 gh = 7² + 2(-10)(0) = 49 – 0 = 49

v_t = √49 = 7 m/s

Te tere whakamutunga i te ahunga whakapae

Ko te tere tīmatanga i te ahunga whakapae ko 7√3 m/s. He pumau te tere, nō reira he rite te tere whakamutunga ki te tere tīmatanga.

Te tere whakamutunga i mua i te pānga o te mea ki te whenua

2. Ka whakatakotoria te tinana ki runga i te koki o te 30^o me te whakapae mai i tētahi whare e 5 mita te teitei. Ko tōna tere tīmatanga he 10 m/s. Tātaihia te tere whakamutunga i mua i te pānga o te mea ki te whenua! Ko te whakaterenga o te kaha ā-papatipu he 10 m/s².

Mōhiotia:

Koki (θ) = 30^o

Teitei tīmatanga (h_o) = 5 mita

Te tere tīmatanga (v_o) = 10 m/s

Te whakaterenga o te kaha ā-papa (g) = 10 m/s²

E hiahiatia ana: Te tere whakamutunga

Rongoā:

Wāhanga whakapae o te tere tīmatanga:

v_ox = v_o cos θ = (10 m/s)(cos 30^o) = (10 m/s)(0.5√3) = 5√3 m / s

Wāhanga poutū o te tere tīmatanga:

v_oy = v_o sin θ = (10 m/s)(sin 30^o) = (10 m/s)(0.5) = 5 m/s

Te tere whakamutunga i te ahunga poutū

Mōhiotia:

Te tere tīmatanga (v_o) = 5 m/s (pai ki runga)

whakaterenga o te kaha ā-papa (g) = –10 m / s² (kino ki raro)

Teitei (h) = -5 m ((kāore i te pai nā te mea kei raro iho te whenua i te teitei tīmatanga)

E hiahiatia ana: Te tere whakamutunga (v_t)

Rongoā:

v_t² = v_o² + 2 gh = 5² + 2(-10)(-5) = 25 + 100 = 125

v_t = √125 m/s

Te tere whakamutunga i te ahunga whakapae

Ko te tere whakamutunga i te ahunga whakapae ko 5√3 m/h

Te tere whakamutunga

3. He pōro iti e tū ana i runga i te whakapae me te tere tīmatanga v_o = 8 m/s mai i tētahi whare 12 mita te teitei. Tātaihia te tere whakamutunga i mua i te pānga o te pōro ki te whenuaKo te tere o te kaha ā-papa he 10 m/s²

Mōhiotia:

Teitei (h) = 12 mita

Te tere tīmatanga (v_o) = 8 m/s

Te whakaterenga o te kaha ā-papa (g) = 10 m/s²

E hiahiatia ana: Te tere whakamutunga (v_t)

Rongoā:

Wāhanga whakapae o te tere tīmatanga:

v_ox = v_o = 8m/s

Wāhanga poutū o te tere tīmatanga:

v_oy = 0m/s

Te tere whakamutunga i te ahunga poutū

i tatauhia mā te whakamahi i te whārite o nekehanga hinga noa.

Mōhiotia:

Te whakaterenga o te kaha ā-papa (g) = 10 m / s²

Teitei (h) = 12 m

E hiahiatia ana: Te tere whakamutunga (v_t)

Rongoā:

v_t² = 2 gh = 2(10)(12) = 240

v_t = √240 m/s

Te tere whakamutunga i te ahunga whakapae

Ko te tere tīmatanga i te ahunga whakapae he 8 m/s. He pumau te tere kia ōrite te tere tīmatanga ki te tere whakamutunga. Nō reira, ko te tere whakamutunga i te ahunga whakapae he 8 m/s.

Te tere whakamutunga

[wpdm_package id='534′]

[wpdm_package id='536′]

1. Whakatauhia te tere tīmatanga ki ngā wāhanga whakapae me ngā wāhanga poutū
2. Whakatauhia te nekehanga whakapae
3. Whakatauhia te teitei mōrahi
4. Whakatauhia te wā
5. Whakatauhia te tūranga o te mea
6. Whakatauhia te tere whakamutunga

Pānuitia atu

Ngā raruraru i whakatauhia i roto i te nekehanga pere - te whakatau i te tūnga o tētahi mea

1. E whakaatuhia ana tētahi tinana ki runga i te koki o te 60^o Tuhinga o mua te whakapae me te tere tīmatanga o te 12 m/s. Tāutuhia te tūranga o te mea i muri i te neke mō te 1 hēkona! Te whakaterenga o te kaha ā-papa he 10 m/s².

Mōhiotia:

Koki (θ) = 60^o

tuatahi tere (v_o) = 12 m/s

Wā wā (t) = 1 hēkona

Te whakaterenga o te kaha ā-papa (g) = 10 m / s²

E hiahiatia ana: Te tūnga o te mea i muri i te neke mō te 1 hēkona

Rongoā:

Wāhanga whakapae o te tere tīmatanga:

v_ox = v_o cos θ = (12 m/s)(cos 60^o) = (12 m/s)(0.5) = 6 m/s

Wāhanga poutū o te tere tīmatanga:

v_oy = v_o sin θ = (12 m/s)(sin 60^o) = (12 m/s)(0.5√3) = 6√3 m / s

Te tūnga o te mea i te ahunga whakapae:

Mōhiotia:

Wāhanga whakapae o te tere (v)_x) = 6 m/s

Wā wā (t) = 1 hēkona

E hiahiatia ana: awhe whakapae (x)

Rongoā:

Ko te tikanga o te 6 mita ia hēkona ka neke te pōro tae atu ki te 6 mita i ia hēkona 1. Ko te tawhiti o te pōro i muri i te neke mō te hēkona 1 he 6 mita. Nō reira, ko te tūranga o te pōro i te ahunga whakapae he 6 mita.

Te tūnga o te mea i te ahunga poutū:

Kōwhiria te ahunga whakarunga hei pai, me te ahunga whakararo hei kino.

Mōhiotia:

Te tere tīmatanga (v_o) = 6√3 m/s (pai ake)

Wā wā (t) = 1 hēkona

Te whakaterenga o te kaha ā-papa (g) = -10 m/s² (kino ki raro)

E hiahiatia ana: teitei i muri i te neke mō te 1 hēkona

Rongoā:

h = v_o t + 1/2 gt² = ((6√3)(1) + 1/2 (-10)(1²) = 6√3 + (-5)(1) = 6√3 – 5 = 6(1.7) – 5 = 10.2 – 5 = 5.2 mita.

Te tūnga o te mea i muri i te neke mō te 1 hēkona:

Nekehanga whakapae (x) = 6 mita

Nekehanga poutū (y) = 5.2 mita

2. E whakaatuhia ana tētahi tinana ki runga i te koki o te 30^o Tuhinga o mua te nekehanga whakapae mai i tētahi whare e 20 mita te teitei. Ko tōna tere tīmatanga he 50 m/s. Tātaihia te nekehanga poutū i muri i te nekehanga o te tinana mō te 1 hēkona! Ko te tere o te kaha ā-papatipu he 10 m/s².

Mōhiotia:

Koki (θ) = 30^o

Teitei tīmatanga (h_o) = 20 mita

Te tere tīmatanga (v_o) = 50 m / s

Wā wā (t) = 1 hēkona

Te whakaterenga o te kaha ā-papa (g) = 10 m / s²

E hiahiatia ana: Teitei (h)

Rongoā:

Wāhanga poutū o te tere tīmatanga:

v_oy = v_o sin θ = (50 m/s)(sin 30^o) = (50 m/s)(0.5) = 25 m / s

Te teitei:

Kōwhiria te ahunga whakarunga hei pai, me te ahunga whakararo hei kino.

Mōhiotia:

Te tere tīmatanga (v_o) = 25 m/s (pai ake)

Wā wā (t) = 1 hēkona

Te whakaterenga o te kaha ā-papa (g) = -10 m / s² (kino ki raro)

E hiahiatia ana: Teitei (h)

Rongoā:

h = v_o t + 1/2 gt² = (25)(1) + 1/2 (-10)(1²) = 25 + (-5)(1) = 25 – 5 = 20 mita.

Ko te teitei o te tinana i muri i te neke mō te 1 hēkona he 20 mita i runga ake i te wāhi e noho ana te tinana. te kaupapa 40 mita rānei i runga ake i te whenua.

3. He pōro iti e tū ana i runga i te whakapae me te tere tīmatanga v_o = 10 m/s mai i tētahi whare he 10 mita te teitei. Tātaihia te nekehanga o te pōro i muri i te nekenga mō te 1 hēkonaKo te tere o te kaha ā-papa he 10 m/s²

Mōhiotia:

Teitei tīmatanga (h) = 10 mita

Te tere tīmatanga (v_o) = 10 m/s

Wā wā (t) = 1 hēkona

Te whakaterenga o te kaha ā-papa (g) = 10 m/s²

Hiahia: Te tūnga o te pōro i muri i te nekenga mō te 1 hēkona!

Rongoā:

Te nekehanga whakapae:

Mōhiotia:

Wāhanga whakapae o te tere (v)_x) = 10 m/s

Wā wā (t) = 1 hēkona

Hiahia: Te tūnga o te mea

Rongoā:

Ko te tikanga o te 10 mita/hekona ka neke te mea tae atu ki te 10 mita i ia 1 hekona. displacement Ko te nekehanga whakapae he 10 mita i muri i te neke mō te 1 hēkona.

Nekehanga poutū:

I tatauhia hei nekehanga hinga noa.

Mōhiotia:

Wā wā (t) = 1 hēkona

Te whakaterenga o te kaha ā-papa (g) = 10 m/s²

E hiahiatia ana: Teitei i muri i te neke mō te 1 hēkona (h)

Rongoā:

h = 1/2 gt² = 1/2 (10)(1²) = (5)(1) = 5 mita.

I muri i te 1 hēkona, ka taka te mea ki te 5 mita te teitei. Teitei ake i te whenua = 10 mita – 5 mita = 5 mita.

Te tūranga o te mea i muri i te nekehanga 1 hēkona:

Te tūnga o te mea i te ahunga whakapae (x) = 10 mita

Ko te tūranga o te mea i te ahunga poutū (y) = 5 mita

[wpdm_package id='532′]

[wpdm_package id='536′]

1. Whakatauhia te tere tīmatanga ki ngā wāhanga whakapae me ngā wāhanga poutū
2. Whakatauhia te nekehanga whakapae
3. Whakatauhia te teitei mōrahi
4. Whakatauhia te wā
5. Whakatauhia te tūranga o te mea
6. Whakatauhia te tere whakamutunga

Pānuitia atu

Ngā raruraru i whakatauhia i roto i te nekehanga pere - whakatau i te wā

1. Ka wehe atu te whutupōro i te whenua i te koki θ = 30^o ki te whakapae me te tere tīmatanga o te 10 m/s. Tātaihia te wā i waenganui i a rātou kia eke ki te teitei mōrahi! Te whakaterenga o te kaha ā-papa he 10 m/s².

Mōhiotia:

Koki (θ) = 30^o

Te tere tīmatanga (v_o) = 10 m/s

Te whakaterenga o te kaha ā-papa (g) = 10 m/s²

E hiahiatia ana: Te wā e tae atu ai ki te teitei rawa

Rongoā:

Wāhanga poutū o te tere tīmatanga:

v_oy = v_o sin θ = (10 m/s)(sin 30^o) = (10 m/s)(0.5) = 5 m / s

Ka whakatauhia te wā hei eke ki te teitei mōrahi e te nekehanga poutū ngā whārite. Kōwhiria te ahunga whakarunga hei pai, me te ahunga whakararo hei kino.

Mōhiotia:

Te tere tīmatanga (v_o) = 5 m / s (pai ake)

Te whakaterenga o te kaha ā-papa (g) = –10 m / s² (kino ki raro)

Te tere whakamutunga i te teitei mōrahi (v_t) = 0

E hiahiatia ana: wā (t)

Rongoā:

v_t = v_o + gt

0 = 5 + (-10)t

0 = 5 – 10 t

5 = 10 tāra

t = 5/10 = 0.5 hēkona

2. E whakaatuhia ana tētahi tinana ki runga i te koki o te 30^o Tuhinga o mua te whakapae me te tere tīmatanga o te 30 m/s. Tātaihia te wā rere! Ko te whakaterenga o te kaha ā-papa he 10 m/s².

Mōhiotia:

Koki (θ) = 30^o

Te tere tīmatanga (v_o) = 8 m/s

Te whakaterenga o te kaha ā-papa (g) = 10 m / s²

E hiahiatia ana: Te wā i mua i te pānga o te tinana ki te whenua

Rongoā:

Wāhanga poutū o te tere tīmatanga:

v_oy = v_o sin θ = (8 m/s)(sin 30^o) = (8 m/s)(0.5) = 4 m / s

Tuatahi ka tatauhia e mātou te wā hei whakatutuki i te teitei mōrahi mā te whakamahi i te whārite o te nekehanga poutū.

Kōwhiria te ahunga whakarunga hei pai, me te ahunga whakararo hei kino.

Mōhiotia:

Te tere tīmatanga (v_o) = 4 m / s (pai ake)

Te whakaterenga o te kaha ā-papa (g) = –10 m / s² (kino ki raro)

Te tere whakamutunga i te teitei mōrahi (v_t) = 0

E hiahiatia ana: Wā wā (t)

Rongoā:

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 i tawhiti atu ai i te teitei mōrahi ko 0.4 hēkona.

Ko te wā i te hau ko 2 x 0.4 s = 0.8 s.

3. E whakaatuhia ana tētahi tinana ki runga i te koki o te 30^o me te whakapae mai i tētahi whare e 10 mita te teitei. Ko tōna tere tīmatanga he 40 m/s. Kia pēhea te roa o te taenga o te tinana ki te whenua? Ko te whakaterenga o te kaha ā-papa he 10 m/s².

Mōhiotia:

Koki (θ) = 30^o

Teitei tīmatanga (h_o) = 10 mita

Te tere tīmatanga (v_o) = 40 m/s

Te whakaterenga o te kaha ā-papa (g) = 10 m / s²

E hiahiatia ana: Te wā i te rangi (t)

Rongoā:

Wāhanga poutū o te tere tīmatanga:

v_oy = v_o sin θ = (40 m/s)(sin 30^o) = (40 m/s)(0.5) = 20 m / s

Tuatahi ka tatauhia e mātou te wā hei whakatutuki i te teitei mōrahi mā te whakamahi i te whārite o te nekehanga poutū.

Kōwhiria te ahunga whakarunga hei pai, me te ahunga whakararo hei kino.

Mōhiotia:

Te tere tīmatanga (v_o) = 20 m / s (pai ake)

Te whakaterenga o te kaha ā-papa (g) = –10 m / s² (kino ki raro)

Te tere whakamutunga i te tihi (v_t) = 0

E hiahiatia ana: Wā wā (t)

Rongoā:

v_t = v_o + gt

0 = 20 + (-10)t

0 = 20 – 10 t

20 = 10 tāra

t = 20/10 = 2 hēkona

Te wā i te rangi = 2 x 2 hēkona = 4 hēkona.

E 10 mita te teitei o te mea i runga ake i te whenua. E 4 hēkona te wā hei tae atu ki tētahi wāhi e whakarara ana ki te tūranga tīmatanga. Kei te neke tonu te pōro ki raro.

Ka tatauhia te wā e tae atu ai ki te whenua mā te whakamahi i te whārite o nekehanga hinga noa. 

Mōhiotia:

Te whakaterenga o te kaha ā-papa (g) = 10 m / s²

Teitei (h) = 10 mita

E hiahiatia ana: Wā wā (t)

Rongoā:

h = 1/2 gt²

10 = 1/2 (10) t²

10 = 5 tāra²

t² = 10/5 = 2

t = √2 = 1.4 hēkona

Wā wā = 1.4 hēkona.

Tapeke wā = 4 hēkona + 1.4 hēkona = 5.4 hēkona.

4. He pōro iti e tū ana i runga i te whakapae me te tere tīmatanga v_o = 15 m/s mai i tētahi whare e 5 mita te teitei. Tātaihia te wā i te rangiKo te tere o te kaha ā-papa he 10 m/s²

Mōhiotia:

Teitei (h) = 5 mita

Te tere tīmatanga (v_o) = 15 m/s

Te whakaterenga o te kaha ā-papa (g) = 10 m/s²

Hiahia: Te wā i te rangi (t)

Rongoā:

Ka tatauhia te wā i te rangi mā te whakamahi i te whārite o te nekehanga e hinga noa ana.

Mōhiotia:

Teitei (h) = 5 mita

Te whakaterenga o te kaha ā-papa (g) = 10 m/s²

E hiahiatia ana: Wā wā (t)

Rongoā:

h = 1/2 gt²

5 = 1/2 (10) t²

5 = 5 tāra²

t² = 5/5 = 1

t = √1 = 1 hēkona

[wpdm_package id='531′]

[wpdm_package id='536′]

1. Whakatauhia te tere tīmatanga ki ngā wāhanga whakapae me ngā wāhanga poutū
2. Whakatauhia te nekehanga whakapae
3. Whakatauhia te teitei mōrahi
4. Whakatauhia te wā
5. Whakatauhia te tūnga o ngā mea
6. Whakatauhia te tere whakamutunga

Pānuitia atu

Ngā raruraru i whakatauhia i roto i te nekehanga pere - whakatau i te teitei mōrahi

1. Ka wehe atu te whutupōro i te whenua i te koki θ = 60^o me te tere tīmatanga o te whakapae he 10 m/s. Tātaihia te teitei mōrahi! Te whakaterenga o te kaha ā-papa he 10 m/s².

Mōhiotia:

Koki (θ) = 60^o

Tere tīmatanga (v_o) = 10 m/s

E hiahiatia ana: Teitei mōrahi (h)

Rongoā:

Wāhanga poutū o te tere tīmatanga:

hara 60^o = v_oy /v_o

v_oy = v_o hara 60^o = (10)(hara 60^o) = (10)(0.5√3) = 5√3 m / s

Kōwhiria te ahunga whakarunga hei pai, me te ahunga whakararo hei kino.

Mōhiotia:

Te whakaterenga o te kaha ā-papa (g) = -10 m/s² (kino ki raro)

Wāhanga poutū o te tere tīmatanga (v)_oy) = +5√3 m / s (pai ake)

Te tere whakamutunga i te teitei mōrahi (v_ty) = 0

E hiahiatia ana: Teitei mōrahi (h)

Rongoā:

v_t² = v_o² + 2 gh

0² = (5√3)² + 2 (-10) hāora

0 = 25(3) – 20 hāora

0 = 75 – 20 hāora

75 = 20 h

h = 75 / 20

h = 3.75 mita

Ko te teitei mōrahi he 3.75 mita.

2. Ka pūhia ake tētahi tinana ki te koki o te 30^o me te whakapae mai i tētahi whare e 20 mita te teitei. Ko tōna tere tīmatanga he 4 m/s. Tātaihia te teitei mōrahi! Ko te whakaterenga o te kaha ā-papatipu he 10 m/s².

Mōhiotia:

Koki (θ) = 30^o

Teitei tīmatanga (h) = 20 mita

Te tere tīmatanga (v_o) = 4 m/s

Te whakaterenga o te kaha ā-papa (g) = 10 m/s²

E hiahiatia ana: Te teitei mōrahi (h)

Rongoā:

Wāhanga poutū o te tere tīmatanga:

hara 30^o = v_oy /v_o

v_oy = v_o hara 30^o = (4)(hara 30^o) = (4)(0.5) = 2 m / s

Kōwhiria te ahunga whakarunga hei pai, me te ahunga whakararo hei kino.

Mōhiotia:

Te whakaterenga o te kaha ā-papa (g) = -10 m/s² (kino ki raro)

Wāhanga poutū o te tere tīmatanga (v)_oy) = +2 m / s (pai ake)

Te tere whakamutunga i te teitei mōrahi (v_ty) = 0

E hiahiatia ana: Te teitei mōrahi

Rongoā:

Te teitei mōrahi:

v_t² = v_o² + 2 gh

0² = 2² + 2 (-10) hāora

0 = 4 – 20 hāora

4 = 20 h

h = 4 / 20

h = 0.2 mita

Ko te teitei mōrahi ko 0.2 mita + 20 mita = 20.2 mita.

[wpdm_package id='528′]

[wpdm_package id='536′]

1. Whakatauhia te tere tīmatanga ki ngā wāhanga whakapae me ngā wāhanga poutū
2. Whakatauhia te nekehanga whakapae
3. Whakatauhia te teitei mōrahi
4. Whakatauhia te wā
5. Whakatauhia te tūnga o ngā mea
6. Whakatauhia te tere whakamutunga

Pānuitia atu

Ngā raruraru i whakatauhia i roto i te nekehanga pere - whakatau i te nekehanga whakapae

1. Ka wehe atu te whutupōro i te whenua i te koki θ = 60^o me te tere tīmatanga o te whakapae he 16 m/s. Kia pēhea te roa i mua i te pa o te pōro ki te whenua?

Mōhiotia:

Koki (θ) = 60^o

Tere tīmatanga (v_o) = 16 m / s

Te whakaterenga o te kaha ā-papa (g) = 10 m/s²

E hiahiatia ana: Nekehanga whakapae (x)

Rongoā:

Wāhanga whakapae o te tere tīmatanga:

v_ox = v_o cos θ = (16 m/s)(cos 60^o) = (16 m/s)(0.5) = 8 m / s

Wāhanga poutū o te tere tīmatanga:

v_oy = v_o sin θ = (16 m/s)(sin 60^o) = (16 m/s)(0.5√3) = 8√3 m / s

Te nekehanga kaupapa Ka taea te mārama mā te tātari motuhake i ngā wāhanga whakapae me ngā wāhanga poutū o te nekehanga. Ka puta te nekehanga x i te tere pumau, ā, ka puta te nekehanga y i te whakaterenga pumau o te kaha ā-papatipu.

Te wā i te rangi

Ko te roa o tōna noho ki te rangi ka whakatauhia e te nekehanga y. Ka kitea tuatahitia te wā mā te whakamahi i te nekehanga y, kātahi ka whakamahia tēnei uara wā ki ngā whārite x (tere pumau whārite).

Kōwhiria te ahunga whakarunga hei pai, me te ahunga whakararo hei kino.

Mōhiotia:

Te tere tīmatanga (v_o) = 8√3 m / s (v_o ki runga)

Te whakaterenga o te kaha ā-papa (g) = -10 m/s² (g ki raro)

Teitei (h) = 0 (kua hoki te pōro ki tōna tūranga kotahi)

E hiahiatia ana: Te wā i te rangi

Rongoā:

h = v_o t + 1/2 gt²

0 = (8√3) t + 1/2 (-10) t²

0 = 8√3 t – 5 t²

8√3 t = 5 t²

8 (1.7) = 5 t

14 = 5 t

t = 14 / 5 = 2.8 hēkona

Nekehanga whakapae

Mōhiotia:

tere (v) = 8 m/s

Wā wā (t) = 2.8 hēkona

E hiahiatia ana: displacement

Rongoā:

x = vt = (8 m/s)(2.8 s) = 22.4 mita

Ko te nekehanga whakapae he 22.4 mita.

2. E whakaatuhia ana tētahi tinana ki runga i te koki o te 60^o me te pou whakapae mai i tētahi whare e 50 mita te teitei. Ko tōna tere tīmatanga he 30 m/s. Tātaihia te nekehanga pou whakapae! Ko te whakaterenga o te kaha ā-papatipu he 10 m/s².

Mōhiotia:

Koki (θ) = 60^o

Teitei (h) = 15 m

Tere tīmatanga (v_o) = 30 m / s

Te whakaterenga o te kaha ā-papa (g) = 10 m/s²

E hiahiatia ana: x

Rongoā:

Wāhanga whakapae o te tere tīmatanga ::

v_ox = v_o cos θ = (30 m/s)(cos 60^o) = (30 m/s)(0.5) = 15 m/s

Wāhanga poutū o te tere tīmatanga:

v_oy = v_o sin θ = (30 m/s)(sin 60^o) = (30 m/s)(0.5√3) = 15√3 m / s

Te wā i te rangi

Ka kimihia te wā mā te whakamahi i te nekehanga y, kātahi ka whakamahia tēnei uara wā ki ngā whārite x (whārite tere pumau). Kōwhiria te piki hei pai, me te heke hei kino.

Mōhiotia:

Te tere tīmatanga (v_o) = 15√3 m / s (pai ake)

Te whakaterenga o te kaha ā-papa (g) = -10 m/s² (kino ki raro)

Teitei (h) = -50 (Te whenua 50 mita i raro i te tūranga tīmatanga)

E hiahiatia ana: t

Rongoā:

h = v_o t + 1/2 gt²

-50 = (15√3) t + 1/2 (-10) t²

-50 = 15√3 t – 5 t²

5 t² - 15√3 t – 50 = 0

Tātaihia te wā mā te whakamahi i tēnei tātai:

a = 5, b = –15√3, c = –50

Ko te wā i te rangi he 6.7 hēkona.

Te nekehanga whakapae:

Mōhiotia:

Tere (v) = 15 m/s

Wā wā (t) = 6.7 hēkona

E hiahiatia ana: Tuhinga

Rongoā:

s = vt = (15 m/s)(6.7 s) = 100.5 mita

Ko te nekehanga whakapae he 100.5 mita.

3. He pōro iti e tū ana i runga i te whakapae me te tere tīmatanga v_o = 10 m/s mai i tētahi whare he 10 mita te teitei. Tātaihia te nekehanga whakapaeKo te tere o te kaha ā-papa he 10 m/s²

Mōhiotia:

Teitei (h) = 10 m

Te tere tīmatanga (v_o) = 10 m / s

Te whakaterenga o te kaha ā-papa (g) = 10 m/s²

E hiahiatia ana: x

Rongoā:

Te wāhanga whakapae o te tere tīmatanga = te tere tīmatanga = 10 m/s.

Te wā i te rangi

Te wā i te rangi i tatauhia mā te whakamahi i nekehanga hinga noa whārite.

Mōhiotia:

Te whakaterenga o te kaha ā-papa (g) = 10 m/s²

Teitei (h) = 10 mita

E hiahiatia ana: t

Rongoā:

h = 1/2 gt²

10 = 1/2 (10) t²

10 = 5 tāra²

t² = 10/5 = 2

t = √2 = 1.4 hēkona

Nekehanga whakapae

Te nekehanga whakapae i tatauhia mā te whakamahi i te whārite o nekehanga i te tere pumau.

Mōhiotia:

Tere (v) = 10 m/s

Wā wā (t) = 1.4 hēkona

E hiahiatia ana: x

Rongoā:

s = vt = (10 m/s)(1.4 s) = 14 mita

Ko te nekehanga whakapae he 14 mita.

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1. Whakatauhia te tere tīmatanga ki ngā wāhanga whakapae me ngā wāhanga poutū
2. Whakatauhia te nekehanga whakapae
3. Whakatauhia te teitei mōrahi
4. Whakatauhia te wā
5. Whakatauhia te tūnga o ngā mea
6. Whakatauhia te tere whakamutunga

Pānuitia atu

Ngā raruraru i whakatauhia i roto i te nekehanga pere - whakatau i te tere tīmatanga ki ngā wāhanga whakapae me ngā wāhanga poutū

1. Ka wehe atu te whutupōro i te whenua i te koki θ = 60^o me te tere o te 10 m/s. Tātaihia ngā wāhanga o te tere tīmatanga!
Mōhiotia:
Koki (θ) = 60^o
Te tere tīmatanga (v_o) = 10 m/s
E hiahiatia ana: v_ox me te v_oy
Rongoā:
Whakatauhia te tere tīmatanga ki te wāhanga x (whakapae) me te wāhanga y (poutū).
hara θ = v_oy /v_o —–> v_oy = v_o hara θ
cos θ = v_ox /v_o —–> v_ox = v_o cos θ

wāhanga x (whakapae) :
v_ox = v_o cos θ = (10 m/s)(cos 60^o) = (10 m/s)(0.5) = 5 m/s

wāhanga y (poutū):
v_oy = v_o sin θ = (10 m/s)(sin 60^o) = (10 m/s)(0.5√3) = 5√3 m/s

2. Ka wehe atu tētahi mea i te whenua i te koki θ = 30^o me te wāhanga y o te tere 10 m/s. Tātaihia te tere tīmatanga!
Mōhiotia:
Koki (θ) = 30^o
wāhanga y (v_oy) = 10 m/s
E hiahiatia ana: Te tere tīmatanga (v_o)
Rongoā:
v_oy = v_o hara θ
10 = (w_o)(hara 30^o)
10 = (w_o)(0.5)
v_o = 10/0.5
v_o = 20m/s

3. Ko te wāhanga whakapae o te tere tīmatanga he 30 m/s, ā, ko te wāhanga poutū o te tere tīmatanga he 40 m/s. Tātaihia te tere tīmatanga.
Mōhiotia:
Wāhanga whakapae o te tere tīmatanga (v_ox) = 30 m/s
Wāhanga poutū o te tere tīmatanga (v)_oy) = 40 m/s
E hiahiatia ana: Te tere tīmatanga (v_o)
Rongoā:
v_o² = v_ox² +v_oy² = 30² + 40² = 900 + 1600 = 2500
v_o = √2500
v_o = 50m/s

4. Ka tukuna whakapaetia tētahi pōro iti me te tere tīmatanga v_o = 6m/s. Tātaihia te wāhanga x me te wāhanga y o te tere tīmatanga.
Mōhiotia:
Te tere tīmatanga (v_o) = 6 m/s
E hiahiatia ana: reo me te v_oy
Rongoā:
Ka neke whakapae te pōro kia rite te wāhanga whakapae o te tere (v)_ox) = te tere tīmatanga (v_o) = 6 m/s. Te wāhanga poutū o te tere (v_oy) = 0.

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1. Whakatauhia te tere tīmatanga ki ngā wāhanga whakapae me ngā wāhanga poutū
2. Whakatauhia te nekehanga whakapae
3. Whakatauhia te teitei mōrahi
4. Whakatauhia te wā
5. Whakatauhia te tūnga o ngā mea
6. Whakatauhia te tere whakamutunga

Pānuitia atu