ahupūngao

1. Ka wehe atu tētahi pōro i whanahia 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 ) = 3 0 ^o

Te tere tīmatanga (v _o ) = 14 m/s

Te whakaterenga o te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana: Te tere whakamutunga i mua i te pānga 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 hara θ = (14 m/s)(hara 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 ake ki runga)

Te whakaterenga o te kaha ā-papa (g) = – 10 m/s ² (kino ki raro)

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

E hiahiatia ana: Te tere whakamutunga ( _vt )

Rongoā:

v _t ² = v _o ² + 2 gh = 7 ² + 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. E whakarewaina ana tētahi tinana ki runga i te koki 30 ^° me te taha 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/s ²

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 hara θ = (10 m/s)(hara 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 ake ki runga)

Te whakaterenga o te kaha ā-papa (g) = – 10 m/s ² (kino ki raro)

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

E hiahiatia ana: Te tere whakamutunga ( _vt )

Rongoā:

v _t ² = v _o ² + 2 gh = 5 ² + 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/s.

Te tere whakamutunga

3. Ka tukuna whakapaetia tētahi pōro iti me te tere tīmatanga v _o = 8 m/s mai i tētahi whare e 12 mita te teitei. Tātaihia te tere whakamutunga i mua i te pa o te pōro ki te whenua ! Ko te tere o te kaha ā-papatipu he 10 m/s ²

Mōhiotia:

Teitei (h) = 12 mita

Te tere tīmatanga (v _o ) = 8 m/s

Te whakaterenga o te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana: Te tere whakamutunga ( _vt )

Rongoā:

Wāhanga whakapae o te tere tīmatanga:

v _ox = v _o = 8 m/s

Wāhanga poutū o te tere tīmatanga:

v _oy = 0 m/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/s ²

Teitei (h) = 12 m

E hiahiatia ana: Te tere whakamutunga ( _vt )

Rongoā:

v _t ² = 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 whakaoti rapanga i roto i te nekehanga pere – te whakatau i te tūranga o tētahi mea

1. E pehia ana tētahi tinana ki runga i te koki 60 ^° ki 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! Ko te tere o te kaha ā-papatipu he 10 m/ ^s².

Mōhiotia:

Koki ( θ ) = 60 ^o

Te tere tīmatanga (v _o ) = 12 m/s

Wā wā (t) = 1 hēkona

Te whakaterenga o te kaha ā-papa (g) = 10 m/s ²

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 hara θ = (12 m/s)(hara 60 ^o ) = (12 m/s)(0.5 √ 3 ) = 6 √ 3 m/s

Te tūnga o te mea i te ahunga whakapae:

Mōhiotia:

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

Wā wā (t) = 1 hēkona

E hiahiatia ana: whānuitanga 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 ki runga)

Wā wā (t) = 1 hēkona

Te whakaterenga o te kaha ā-papa (g) = -10 m/s ² (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

[irp]

2. E whakarewaina ana tētahi tinana ki runga i te koki 30 ^° ki te 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 neke 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) = 1 0 m/s ²

Teitei e hiahiatia ana: Teitei (h)

Rongoā:

Wāhanga poutū o te tere tīmatanga:

v _oy = v _o hara θ = (50 m/s)(hara 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 ki runga)

Wā wā (t) = 1 hēkona

Te whakaterenga o te kaha ā-papa (g) = -1 0 m/s ² (kino ki raro)

Teitei e hiahiatia ana: Teitei (h)

Rongoā:

h = v _o t + 1/2 gt ^{​​​​2} = (25)(1) + 1/2 (-10)(1 ² ) = 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 whakatakotoria ana te tinana , he 40 mita rānei i runga ake i te whenua.

[irp]

3. Ka tukuna whakapaetia tētahi pōro iti me te tere tīmatanga v _o = 10 m/s mai i tētahi whare 10 mita te teitei. Tātaihia te nekehanga o te pōro i muri i te neke i roto i te 1 hēkona ! Ko te tere o te kaha ā-papatipu he 10 m/s ²

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/s ²

E hiahiatia ana: Te tūranga o te pōro i muri i te nekenga mō te 1 hēkona!

Rongoā:

Te nekehanga whakapae:

Mōhiotia:

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

Wā wā (t) = 1 hēkona

E hiahiatia ana: Te tūnga o te mea

Rongoā:

Ko te tikanga o te 10 mita/hēkona ka neke te mea tae atu ki te 10 mita i ia 1 hēkona. Ko te nekehanga i muri i te nekehanga mō te 1 hēkona he 10 mita. Nō reira, ko te nekehanga whakapae he 10 mita.

Nekehanga poutū:

I tatauhia hei nekehanga hinga noa.

Mōhiotia:

Wā wā (t) = 1 hēkona

Te whakaterenga o te kaha ā-papa (g) = 10 m/s ²

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

Rongoā:

h = 1/2 gt ^{​​​​2} = 1/2 (10)(1 ² ) = (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

[irp]

[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 rapanga kua whakatauhia i roto i te nekehanga pere – te whakatau i te wā

1. Ka wehe atu tētahi 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 ia me te eke ki te teitei mōrahi! Ko te whakaterenga o te kaha ā-papatipu he 10 m/ ^s2.

Mōhiotia:

Koki (θ) = 3 0 ^o

Te tere tīmatanga (v _o ) = 10 m/s

Te whakaterenga o te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana: Te wā hei whakatutuki i te teitei mōrahi

Rongoā:

Wāhanga poutū o te tere tīmatanga:

v _oy = v _o hara θ = (10 m/s)(hara 30 ^o ) = (10 m/s)(0.5) = 5 m/s

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

Mōhiotia:

Te tere tīmatanga (v _o ) = 5 m/s (pai ake ki runga)

Te whakaterenga o te kaha ā-papa (g) = – 10 m/s ² (kino ki raro)

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

E hiahiatia ana: te wā (t)

Rongoā:

vt = v _{o +} g t

0 = 5 + (-10)t

0 = 5 – 10 t

5 = 10 tāra

t = 5/10 = 0.5 hēkona

[irp]

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

Mōhiotia:

Koki (θ) = 3 0 ^o

Te tere tīmatanga (v _o ) = 8 m/s

Te whakaterenga o te kaha ā-papa (g) = 10 m/s ²

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 hara θ = (8 m/s)(hara 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 ki runga)

Te whakaterenga o te kaha ā-papa (g) = – 10 m/s ² (kino ki raro)

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

E hiahiatia ana: Te wā (t)

Rongoā:

vt = v _{o +} g t

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.

[irp]

3. E whakarewaina ana tētahi tinana ki runga i te koki o te 30 ^° me te taha 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 tere o te kaha ā-papatipu he 10 m/ ^s².

Mōhiotia:

Koki (θ) = 3 0 ^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/s ²

E hiahiatia ana: Te wā i te rangi (t)

Rongoā:

Wāhanga poutū o te tere tīmatanga:

v _oy = v _o hara θ = (40 m/s)(hara 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 ki runga)

Te whakaterenga o te kaha ā-papa (g) = – 10 m/s ² (kino ki raro)

Te tere whakamutunga i te tihi (vt ₎ = 0

E hiahiatia ana: Te wā (t)

Rongoā:

vt = v _{o +} g t

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 ai ki te whenua mā te whakamahi i te whārite o te nekehanga hinga noa.

Mōhiotia:

Te whakaterenga o te kaha ā-papa (g) = 10 m/s ²

Teitei (h) = 10 mita

E hiahiatia ana: Te wā (t)

Rongoā:

h = 1/2 gt ^{​​​​2}

10 = 1/2 (10) t ²

10 = 5 t ²

t ² = 10/5 = 2

t = √2 = 1.4 hēkona

Wā wā = 1.4 hēkona.

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

[irp]

4. Ka tukuna whakapaetia tētahi pōro iti me te tere tīmatanga v _o = 15 m/s mai i tētahi whare e 5 mita te teitei. Tātaihia te wā i te rangi ! Ko te whakaterenga o te kaha ā-papa he 10 m/s ²

Mōhiotia:

Teitei (h) = 5 mita

Te tere tīmatanga (v _o ) = 15 m/s

Te whakaterenga o te kaha ā-papa (g) = 10 m/s ²

E hiahiatia ana: 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/s ²

E hiahiatia ana: Te wā (t)

Rongoā:

h = 1/2 gt ^{​​​​2}

5 = 1/2 (10) t ²

5 = 5 t ²

t ² = 5/5 = 1

t = √1 = 1 hēkona

[irp]

[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 kua whakatauhia i roto i te nekehanga pere – te whakatau i te teitei mōrahi

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

Mōhiotia:

Koki (θ) = 60 ^o

Tere tīmatanga (v _o ) = 10 m/s

Teitei mōrahi (h)

Rongoā:

Wāhanga poutū o te tere tīmatanga:

sin 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/s ² (kino ki raro)

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

Te tere whakamutunga i te teitei mōrahi (v _ty ) = 0

Teitei mōrahi (h)

Rongoā:

vt ₂ = v _o ^{2 + 2} gh

0 ² = ( 5 √ 3) ² + 2 (-10) hāora

0 = 2 5 ( 3) – 20 hāora

0 = 75 – 20 hāora

75 = 20 hāora

h = 75 / 20

h = 3.75 mita

Ko te teitei mōrahi he 3.75 mita.

[irp]

2. E whakarewaina ana tētahi tinana ki runga i te koki o te 30 ^° me te taha 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/s ²

E hiahiatia ana: Te teitei mōrahi (h)

Rongoā:

Wāhanga poutū o te tere tīmatanga:

sin 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/s ² (kino ki raro)

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

Te tere whakamutunga i te teitei mōrahi (v _ty ) = 0

E hiahiatia ana: Te teitei mōrahi

Rongoā:

Te teitei mōrahi:

vt ₂ = v _o ^{2 + 2} gh

0 ² = 2 ² + 2 (-10) hāora

0 = 4 – 20 hāora

4 = 20 hāora

h = 4 / 20

h = 0.2 mita

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

[irp]

[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 rapanga kua whakatauhia i roto i te nekehanga pere – te whakatau i te nekehanga whakapae

1. Ka wehe atu tētahi pōro i te whenua i te koki θ = 60 ^° , ā, ko te tere tīmatanga o te poutū he 16 m/s. Kia pēhea te roa i mua i te pānga 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/s ²

E hiahiatia ana: Te 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 hara θ = (16 m/s)(hara 60 ^o ) = (16 m/s)(0.5 √ 3 ) = 8 √ 3 m/s

Ka taea te mārama ki te nekehanga pere 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-papa.

Te wā i te rangi

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

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/s ² (g ki raro)

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

E hiahiatia ana: Te Wā i te Rererangi

Rongoā:

h = v _o t + 1/2 gt ^{​​​​2}

0 = ( 8 √ 3) t + 1/2 (-10) t ²

0 = 8 √ 3 t – 5 t ²

8 √ 3 t = 5 t ²

8 (1.7) = 5 t

14 = 5 tāra

t = 14 / 5 = 2.8 hēkona

Nekehanga whakapae

Mōhiotia:

Tere (v) = 8 m/s

Wā wā (t) = 2.8 hēkona

E hiahiatia ana: Te nekehanga

Rongoā:

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

Ko te nekehanga whakapae he 22.4 mita.

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2. E whakarewaina ana tētahi tinana ki runga i te koki 60 ^° me te taha whakapae mai i tētahi whare e 50 mita te teitei. Ko tōna tere tīmatanga he 30 m/s. Tātaihia te nekehanga 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/s ²

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 hara θ = (30 m/s)(hara 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 ki runga)

Te whakaterenga o te kaha ā-papa (g) = -10 m/s ² (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 gt ^{​​​​2}

-50 = ( 15 √ 3 ) t + 1/2 (-10) t ²

-50 = 15 √ 3 t – 5 t ²

5 t ² – 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: te nekehanga

Rongoā:

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

Ko te nekehanga whakapae he 100.5 mita.

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3. Ka tukuna whakapaetia tētahi pōro iti me te tere tīmatanga v _o = 10 m/s mai i tētahi whare 10 mita te teitei. Tātaihia te nekehanga whakapae ! Ko te whakaterenga o te kaha ā-papatipu he 10 m/s ²

Mōhiotia:

Teitei (h) = 10 m

Te tere tīmatanga (v _o ) = 10 m/s

Te whakaterenga o te kaha ā-papa (g) = 10 m/s ²

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

Mōhiotia:

Te whakaterenga o te kaha ā-papa (g) = 10 m/s ²

Teitei (h) = 10 mita

E hiahiatia ana: t

Rongoā:

h = 1/2 gt ^{​​​​2}

10 = 1/2 (10) t ²

10 = 5 t ²

t ² = 10 / 5 = 2

t = √2 = 1.4 hēkona

Nekehanga whakapae

Ka tatauhia te nekehanga whakapae mā te whakamahi i te whārite o te 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

I whakatauhia ngā raruraru i roto i te nekehanga pere – i whakatauhia te tere tīmatanga ki ngā wāhanga whakapae me te 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

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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

[irp]

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

[irp]

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