Tauira o te Nekehanga Raina Whakatere Taurite (GLBB)
He kaupapa nui te Nekehanga Raina Whakateretere Taurite (GLBB) i roto i te ahupūngao e puta pinepine ana i ngā akoranga kura tuarua. Ko te GLBB te nekehanga o tētahi mea i roto i tētahi rārangi tika me te whakaterenga pumau. I roto i tēnei tuhinga, ka matapakihia e mātou te whakamāramatanga, ngā tātai taketake, me ētahi tauira o ngā raruraru GLBB me ō rātou otinga.
Te Whakamāramatanga o te Nekehanga Raina Whakatere Taurite (GLBB)
Ko te Nekehanga Raina Whakateretere Taurite (GLBB) te nekehanga o tētahi mea i runga i tētahi rārangi tika me te whakaterenga pumau. Ko te whakaterenga pumau ko te tere o te huringa o te tere o te mea ka noho pumau tonu i roto i te wā. Ka taea te wehewehe i te GLBB kia rua ngā momo:
1. GLBB Whakateretere: Ka pāngia te mea e te whakateretere pai (ka piki te tere).
2. GLBB Whakaroa: Ka pāngia te mea e te whakaterenga kino (ka heke te tere).
Te Tātai Taketake mō te GLBB
Ko ētahi o ngā tātai taketake i roto i te GLBB e whakamahia pinepinetia ana ko:
1. Tātai tere whakamutunga (v):
\[ v = v_0 + i \]
Kei hea:
– \( v \) = tere whakamutunga (m/s)
– \( v_0 \) = te tere tīmatanga (m/s)
– \( a \) = whakaterenga (m/s²)
– \( t \) = wā (s)
2. Tātai tawhiti (ngā tātai):
\[ s = v_0 t + \frac{1}{2} i^2 \]
Kei hea:
– \( s \) = te tawhiti i haerea (m)
– \( v_0 \) = te tere tīmatanga (m/s)
– \( a \) = whakaterenga (m/s²)
– \( t \) = wā (s)
3. Te tātai mō te tere me te tawhiti i haerea:
\[ v^2 = v_0^2 + 2 hei \]
Kei hea:
– \( v \) = tere whakamutunga (m/s)
– \( v_0 \) = te tere tīmatanga (m/s)
– \( a \) = whakaterenga (m/s²)
– \( s \) = te tawhiti i haerea (m)
Tauira o ngā Raru me ngā Otinga GLBB
Anei ētahi tauira o ngā raruraru GLBB me ngā mahi hei whakaoti rapanga.
Tauira Pātai 1
Pātai:
E neke ana tētahi motuka me te tere tīmatanga o te 20 m/s, ā, ka tere ake te whakaterenga o te 2 m/s². Tātaihia te tere o te motuka i muri i te 5 hēkona!
Otinga:
E mōhiotia ana:
– Te tere tīmatanga (\( v_0 \)) = 20 m/s
– Te whakaterenga (\( a \)) = 2 m/s²
– Te Wā (\( t \)) = 5 hēkona
Mā te whakamahi i te tātai tere whakamutunga:
\[ v = v_0 + i \]
\[ v = 20 + (2 \whakanuia te 5) \]
\[ v = 20 + 10 \]
\[ v = 30 \, \text{m/s} \]
Nō reira, ko te tere o te motuka i muri i te 5 hēkona ko 30 m/s.
Tauira Pātai 2
Pātai:
Ko te tere tīmatanga o tētahi mea e neke ana he 10 m/s ka pāngia e te whakaterenga o te -3 m/s². Tātaihia te tawhiti i haerea e te mea i roto i te 4 hēkona.
Otinga:
E mōhiotia ana:
– Te tere tīmatanga (\( v_0 \)) = 10 m/s
– Te whakaterenga (\( a \)) = -3 m/s²
– Te Wā (\( t \)) = 4 hēkona
Mā te whakamahi i te tātai tawhiti:
\[ s = v_0 t + \frac{1}{2} i^2 \]
\[ s = (10 \times 4) + \frac{1}{2} (-3) (4)^2 \]
\[ s = 40 + \frac{1}{2} (-3) \times 16 \]
\[ s = 40 – 24 \]
\[ s = 16 \, \kuputuhi{m} \]
Nō reira, ko te tawhiti i haerea e te mea i roto i te 4 hēkona he 16 mita.
Tauira Pātai 3
Pātai:
Ka whakaterea te motopaika e tū ana i te tīmatanga (ko te tere tīmatanga 0 m/s) i te tere o te 5 m/s². Tātaihia te tere o te motopaika i muri i te haerenga i te tawhiti o te 50 mita.
Otinga:
E mōhiotia ana:
– Te tere tīmatanga (\( v_0 \)) = 0 m/s
– Te whakaterenga (\( a \)) = 5 m/s²
– Te tawhiti i haerea (\( s \)) = 50 mita
Mā te whakamahi i te tātai tere me te tawhiti:
\[ v^2 = v_0^2 + 2 hei \]
\[ v^2 = 0 + 2 \whakareatia ki te 5 \whakareatia ki te 50 \]
\[ v^2 = 500 \]
\[ v = \sqrt{500} \]
\[ v = 22,36 \, \text{m/s} \]
Nō reira, ko te tere o te motopaika i muri i te haere i te tawhiti o te 50 mita ko 22,36 m/s.
Tauira Pātai 4
Pātai:
E neke ana tētahi mea me te tere tīmatanga o te 15 m/s, ā, ka pāngia e te whakahekenga o te 4 m/s² tae noa ki tōna tūnga. Kia pēhea te roa ka mutu te mea?
Otinga:
E mōhiotia ana:
– Te tere tīmatanga (\( v_0 \)) = 15 m/s
– Te tere whakamutunga (\( v \)) = 0 m/s
– Te whakaterenga (\( a \)) = -4 m/s²
Mā te whakamahi i te tātai tere whakamutunga:
\[ v = v_0 + i \]
\[ 0 = 15 + (-4) t \]
\[ -15 = -4 t \]
\[ t = \frac{15}{4} \]
\[ t = 3,75 \, \text{hēkona} \]
Nō reira, ko te wā e pau ana i te mea kia tū ai ko 3,75 hēkona.
Tauira Pātai 5
Pātai:
Ko te tere tīmatanga o tētahi waka he 25 m/s, ā, ka tere ake te whakaterenga o te 3 m/s² mō te 6 hēkona. Tātaihia te tawhiti i haerea e te waka i roto i tēnei wā.
Otinga:
E mōhiotia ana:
– Te tere tīmatanga (\( v_0 \)) = 25 m/s
– Te whakaterenga (\( a \)) = 3 m/s²
– Te Wā (\( t \)) = 6 hēkona
Mā te whakamahi i te tātai tawhiti:
\[ s = v_0 t + \frac{1}{2} i^2 \]
\[ s = (25 \times 6) + \frac{1}{2} (3) (6)^2 \]
\[ s = 150 + \frac{1}{2} (3) \times 36 \]
\[ s = 150 + 54 \]
\[ s = 204 \, \kuputuhi{m} \]
Nō reira, ko te tawhiti i haerea e te motuka i roto i te 6 hēkona he 204 mita.
Whakamutunga
Ko te Nekehanga Raina Whakateretere Taurite (GLBB) he ariā nui i roto i te ahupūngao e whakaahua ana i te nekehanga o tētahi mea me te whakaterenga pumau. Ko te mārama ki ngā tātai taketake o te GLBB me te āhei ki te whakamahi i aua tātai ki ngā āhuatanga rerekē he pūkenga nui i roto i te ahupūngao. Mā roto i ngā tauira i runga ake nei, ka taea e tātou te kite me pēhea te whakamahi i ēnei tātai hei tatau i te tere, te tawhiti, me te wā i raro i ngā āhuatanga nekehanga rerekē. Mēnā he nui te mahi, ka taea te whakapakari i tēnei māramatanga o te GLBB me te whakamahi ki ngā raruraru ahupūngao uaua ake.
