Ngā tātai taputapu whatu mō ngā whakaata me ngā karāhe

Ngā tauira pātai me ngā tātai mō ngā taputapu whatu, ngā whakaata me ngā karāhe arotahi

Whakaata papatahi

1. Kei mua i ngā whakaata papatahi e rua tētahi rama, e hanga ana i tētahi koki o te 60 ^° tetahi ki tetahi , kātahi ka ko te maha o ngā whakaahua o te rama ko....

1. 3 hua
2. 4 hua
3. 5 hua
4. 6 hua

Kōrero
Mātakitakihia ngā whakaahua e rua i raro nei. Kei mua i te mata whakaata te mea (porowhita matomato) e whakaata ana i te mārama. Ko ngā hihi mārama e puta mai ana i te mea ki te whakaata papatahi e poutū ana ki te mata whakaata papatahi, e hanga ana i te koki 90-tohu.^oE ai ki te ture whakaata o te mārama, he ōrite te koki pānga ki te koki whakaata.

Mena he 90 te koki o te putanga^o kātahi ka 90 hoki te koki whakaata^o.
I te ahua maui, kei waenganui i ngā whakaata papatahi e rua te mea, ā, e rua ngā ahua ka hangaia. I te ahua matau, kei te tata atu te mea ki tētahi o ngā whakaata papatahi, ā, e toru ngā ahua ka hangaia.
Ko te whakautu tika ko A.

Whakaata kōpiko

2. Ka tirotirohia, ka tirohia hoki e te tākuta niho te kōhao niho o muri o te tūroro mā te whakamahi i tētahi whakaata he 8 henimita te whānui. Kia mārama ai te kite i te kōhao o te tūroro, kia nui hoki, e te tākuta niho, me tū te niho o te tūroro ki mua i te whakaata i te tawhiti o...

1. iti iho i te 4 henimita ki mua i te whakaata kōpiko
2. iti iho i te 4 henemita ki mua i te whakaata pūkohu
3. neke atu i te 4 henimita ki mua i te whakaata kōpiko
4. neke atu i te 4 henemita ki mua i te whakaata pūkohu

Kōrero
E mōhiotia ana:
Te pūtoro whakaata (r) = 8 cm
Te roa o te arotahi o te whakaata (f) = r / 2 = 8 / 2 = 4 cm
I pātaihia: Kia pēhea te tawhiti o ngā niho o te tūroro i roto i te whakaata?
Whakautu:
He whakaata piko, he whakaata pūkohu rānei te whakaata e whakamahia ana? I roto i te pātai tuhituhi kia taea ai te horoi i te kōhao niho o te tūroro mārama te kitea dan nui rawa e te tākuta Nō reira, me kaha te whakaata e whakamahia ana ki te whakanui i te ahua o ngā niho o te tūroro, ā, me tū tika te ahua. Ka puta he ahua hurihuri i ngā whakaata pūkohu, ā, he iti ake te rahi o te ahua i te rahi o te mea. I tetahi atu taha, ka taea e te whakaata piko te whakaputa i tētahi ahua tū tika mēnā he iti ake te tawhiti (s) o te mea i te roa arotahi (f). Mēnā he nui ake te tawhiti o te mea i te roa arotahi (f), ka puta he ahua hurihuri i te whakaata piko.
Ko te roa arotahi (f) o te whakaata piko he 4 cm, nō reira me iti iho i te 4 cm te tawhiti o ngā niho o te tūroro ki mua i te whakaata piko.
Ko te whakautu tika ko A.

3. Ko te radius piko o te whakaata kōpiko he 24 cm. Mena ka whakatakotoria he mea 20 cm ki mua i te whakaata, ko te ahua ka puta ko...

1. tūturu, poutū, me te whakanui
2. tūturu, hurihia, whakanuia
3. mariko, poutū me te whakanuia
4. mariko, hurihia me te whakaiti

Kōrero
E mōhiotia ana:
Te whānui o te piko (r) = 24 cm
Roanga arotahi (f) = R/2 = 24/2 = +12 cm
He pai, he tūturu rānei te roa arotahi o te whakaata kōpiko nā te mea ka haere te hihi mārama mā te pūwāhi arotahi o te whakaata kōpiko.
Te tawhiti o te mea (s) = 20 cm
I pātaihia: Ngā āhuatanga o ngā atarangi
Whakautu:
He mariko, he tūturu rānei te ahua? Hei kimi i tēnei, tātaihia te tawhiti (s') o te ahua:
1/s + 1/s' = 1/f
1/s' = 1/f – 1/s
1/s' = 1/12 – 1/20
1/s' = 5/60 – 3/60
1/s' = 2/60
s' = 60/2
s' = 30 henemita
He pai te tawhiti o te atarangi, arā, he tūturu te atarangi nā te mea ka whiti te mārama mā roto (whakatairite ki te ahua kei te taha).

Kua whakanuia, kua whakaitihia rānei te ahua? Kei te poutū, kei te huripokitia rānei te ahua? Hei kimi i tēnei, tatauhia te whakanuinga o te ahua (M):
M = -s' / s = -30/20 = -1,5
M > 1 te tikanga kua whakanuia te ahua, ko M he kino te tikanga kua hurihia te ahua (whakatairitea ki te ahua kei te taha). Nō reira, ko ngā āhuatanga o te ahua he tūturu, he hurihia, he whakanuia
Ko te whakautu tika ko B.

Whakaata kōpiko

4. Ko te mārama e tau ana ki runga i te whakaata pūkohu i te ahunga e whakarara ana ki te tuaka matua o te whakaata ka whakaatahia….

1. ki te pūwāhi arotahi o te whakaata
2. me te mea mai i te pūwāhi arotahi o te whakaata
3. mā roto i te pokapū o te piko o te whakaata
4. poutū ki te papa o te whakaata

Kōrero
Mātakitaki i te pikitia kei te taha.

Ko te whakautu tika ko B.

5. Ka kite te kaieke motopaika i te atarangi o te waka i muri i a ia, he 1/6 o tōna rahi tuturu. Mena he 30 mita te tawhiti i waenganui i te taraiwa me te waka i muri i a ia, ka whakamahia e te whakaata tirohanga whakamuri o te motopaika he whakaata me te radius piko o...

1. 7,14 m
2. 8,57 m
3. 12,00 m
4. 24,00 m

Kōrero
E mōhiotia ana:
Whakanuia o te ahua (M) = 1/6 ngā wā
Te tawhiti o te mea (s) = 30 mita
I pātaihia: Te whānui o te piko o te whakaata tirohanga whakamuri pūkohu (R)
Whakautu:
Tātaihia te tawhiti atarangi (s')
Nā te mea e mōhiotia ana te whakanui o te ahua (M) me te tawhiti o te mea (s), ka taea te whakatau i te tawhiti o te ahua mā te whakamahi i te tātai whakanui o te ahua:

Ko te tohu kino he tohu mariko te ahua. E 5 mita te tawhiti o te ahua i muri i te whakaata pūkohu.

Tātaihia te roa arotahi (f)
Nā te mea e mōhiotia ana te tawhiti o te mea (s) me te tawhiti o te ahua (s'), ka taea te tatau i te roa arotahi mā te whakamahi i te tātai whakaata piko:

Tātaihia te pūtoro o te piko (R)
Ko te pūtoro o te piko o te whakaata pūkohu e rua te roa o te arotahi o te whakaata pūkohu.
R = 2 f = 2 (6 mita) = 12 mita
Ko te radius o te piko o te whakaata tirohanga whakamuri kōpikopiko he 12 mita.
Ko te whakautu tika ko C.

Karāhe kōpiko

6. Kei te tawhiti atu i te 50 cm te tawhiti o tētahi karu arotahi pai, he 25 cm te roa o te arotahi. Ko te āhua o te ahua ka puta ko…..

1. tūturu, hurihia, whakanuia
2. mariko, poutū, ā, he rite te rahi ki te mea
3. mariko, poutū me te whakanuia
4. tūturu, hurihia, ā, he rite te rahi ki te mea

Kōrero
E mōhiotia ana:
Te tawhiti o te mea (s) = 50 cm
Te roa o te arotahi o te karu (f) = +25 cm
He pai te roa arotahi nā te mea he karaihe pai, he karaihe pūkohu rānei te karaihe e whakamahia ana.
I pātaihia: Ko te āhua o ngā atarangi he…
Whakautu:
He mariko, he tūturu rānei te atarangi? Hei kimi i tēnei, tātaihia te tawhiti o te atarangi:
1/s' = 1/f – 1/s
1/s' = 1/25 – 1/50
1/s' = 2/50 – 1/50
1/s' = 1/50
s' = 50/1
s' = 50 henemita
He pai te tawhiti o te atarangi, arā, he tūturu te atarangi nā te mea ka tika te mārama mā roto.

Kua whakanuia, kua whakaitihia rānei te ahua? He poutū, he huripokitia rānei te ahua? Hei kimi i tēnei, tatauhia te whakanuinga o te ahua:
M = -s' / s = -50/50 = -1
Ko te tikanga o te M = 1 he rite te rahi o te atarangi ki te mea
He tōraro a M, arā, kua hurihia te ahua.

Nō reira, he tūturu te āhua o te atarangi, he huripokitia, ā, he rite te rahi ki te mea.
Ko te whakautu tika ko D.

Pūtake pātai:

Ngā Pātai OSN mō te Ahupūngao o te Kura Tuarua