Ngā Tauira Pātai me te Kōrero mō ngā Tikanga Nekehanga
Ko te tikanga nekehanga, arā, ko te tikanga o te nekehanga, he peka o te ahupūngao e ako ana i te nekehanga o ngā mea me ngā kaha e puta ai taua nekehanga. He mea nui te mārama ki te tikanga o te nekehanga hei whakaoti rapanga i roto i te ahupūngao me te hangarau. I roto i tēnei tuhinga, ka matapakihia e mātou ētahi tauira rapanga mō te tikanga o te nekehanga me ō rātou otinga.
Tauira Pātai 1: Nekehanga Raina Ā-Rohe (GLB)
Pātai: E neke ana tētahi motuka i te tere pumau o te 60 km/h i runga i te rori tika mō ngā hāora e 2. Kia pēhea te tawhiti e haere ai te motuka?
Kōrero:
Ko te Nekehanga Raina Āhua (GLB) te nekehanga o tētahi mea i te tere pumau. Ko te tātai e whakamahia ana hei tatau i te tawhiti i roto i te GLB ko:
\[ \text{Tawhiti} = \text{Tere} \times \text{Wā} \]
E mōhiotia ana:
– Tere = 60 kiromita/h
– Te wā = 2 hāora
Te tatau i te tawhiti:
\[ \text{Tawhiti} = 60 \, \text{km/h} \times 2 \, \text{h} = 120 \, \text{km} \]
Nō reira, ko te tawhiti i haerea e te motuka he 120 km.
Tauira Pātai 2: Nekehanga Raina Whakatere Taurite (GLBB)
Pātai: E neke ana tētahi mea me te whakaterenga pumau o te 2 m/s² mai i te okiokinga. He aha te tere o te mea i muri i te 5 hēkona?
Kōrero:
Ko te Nekehanga Raina Whakatere Taurite (GLBB) he nekehanga e huri tonu ana te tere me te whakaterenga pumau. Ko te tātai mō te tatau i te tere whakamutunga mai i te okiokinga ko:
\[ v = u + i \]
Kei hea:
– Ko te tere whakamutunga ko \( v \)
– Ko te tere tīmatanga ko \( u \) (u = 0, nā te mea mai i te āhua okiokinga)
– Ko te whakaterenga te \( a \)
– ko te wā ko te \( t \)
E mōhiotia ana:
– \( u = 0 \)
– \( a = 2 \, \kuputuhi{m/s}^2 \)
– \( t = 5 \, \kuputuhi{s} \)
Te tatau i te tere whakamutunga:
\[ v = 0 + (2 \, \text{m/s}^2 \times 5 \, \text{s}) = 10 \, \text{m/s} \]
Nō reira, ko te tere o te mea i muri i te 5 hēkona ko 10 m/s.
Tauira Pātai 3: Nekehanga Hinga Noa
Pātai: Ka taka tetahi pōro mai i te teitei o te 45 mita. Kia pēhea te roa ka tae te pōro ki te whenua? (Kaua e aro ki te ātete hau, whakamahia te whakaterenga nā te kaha ā-papa \( g = 9.8 \, \text{m/s}^2 \)).
Kōrero:
Mō te nekehanga hinga noa, ka whakamahia e mātou te tātai:
\[ h = \frac{1}{2}gt^2 \]
Kei hea:
– Ko te teitei ko te \( h \)
– Ko te whakaterenga nā te kaha ā-papatipu te \( g \)
– ko te wā ko te \( t \)
E mōhiotia ana:
– \( h = 45 \, \kuputuhi{m} \)
– \( g = 9.8 \, \text{m/s}^2 \)
Whakakapia ēnei uara ki roto i te tātai:
\[ 45 = \frac{1}{2} \times 9.8 \times t^2 \]
\[ 45 = 4.9 \whakanuia ki te t^2 \]
\[ t^2 = \frac{45}{4.9} \]
\[ t^2 \tata ki te 9.18 \]
\[ t \tata ki te 3.03 \, \kuputuhi{s} \]
Nō reira, ko te wā e pau ana mō te pōro ki te tau ki te whenua he 3.03 hēkona pea.
Tauira Pātai 4: Nekehanga Porowhita
Pātai: E neke ana tētahi mea i roto i tētahi porowhita, ko te radius he 2 mita, ā, ko te tere koki he 4 rad/s. He aha tōna tere rārangi?
Kōrero:
Ka taea te tatau i te tere rārangi i roto i te nekehanga porowhita mā te whakamahi i te tātai:
\[ v = \omega r \]
Kei hea:
– Ko te tere rārangi te \( v \)
– Ko te tere koki te \( \omega \)
– Ko te radius te \( r \)
E mōhiotia ana:
– \( \omega = 4 \, \text{rad/s} \)
– \( r = 2 \, \kuputuhi{m} \)
Te tatau i te tere rārangi:
\[ v = 4 \, \text{rad/s} \times 2 \, \text{m} = 8 \, \text{m/s} \]
Nō reira, ko te tere rārangi o te mea he 8 m/s.
Tauira Pātai 5: Nekehanga Parabolic
Pātai: Ka whanahia tētahi pōro me te tere tīmatanga o te 20 m/s i te koki o te 30° ki te whakapae. He aha te tawhiti whakapae mōrahi ka taea e te pōro te tae atu?
Kōrero:
Mō te nekehanga parabolic, ka taea te tatau i te tawhiti whakapae mōrahi (awhe) mā te whakamahi i te tātai:
\[ R = \frac{v_0^2 \sin 2\theta}{g} \]
Kei hea:
– Ko te tawhiti whakapae mōrahi ko \( R \)
– Ko te tere tīmatanga ko \( v_0 \)
– Ko te koki teitei te \( \theta \)
– Ko te whakaterenga nā te kaha ā-papatipu te \( g \)
E mōhiotia ana:
– \( v_0 = 20 \, \kuputuhi{m/s} \)
– \( \theta = 30^\circ \)
– \( g = 9.8 \, \text{m/s}^2 \)
Te tatau i te tawhiti whakapae mōrahi:
\[ R = \frac{20^2 \times \sin(60^\circ)}{9.8} \]
\[ R = \frac{400 \times \sqrt{3}/2}{9.8} \]
\[ R = \frac{400 \times 0.866}{9.8} \]
\[ R \tata \frac{346.4}{9.8} \]
\[ R \tata ki te 35.34 \, \kuputuhi{m} \]
Nō reira, ko te tawhiti whakapae mōrahi ka taea e te pōro te tae atu ko te 35.34 mita.
Whakamutunga
I roto i tēnei tuhinga, kua matapakihia e mātou ētahi tauira raruraru e whakaatu ana i te whakamahinga o ngā mātāpono taketake o te nekehanga i roto i te ahupūngao. He mea nui te mārama ki ēnei ariā mō ngā ākonga me ngā tohunga ngaio ki te tātari me te matapae i te nekehanga o ngā mea o te ao tūturu. Ko te tumanako, ka whai hua ēnei tauira mō te hunga e hiahia ana ki te mārama ake ki ngā hihiri o te nekehanga.
