Ngā Tauira Pātai me te Kōrero mō te Tāpiri i ngā Wētera e Rua mā te Whakamahi i te Tikanga Tapatoru
Pendahuluan
He rahinga kei a ia te rahi me te ahunga o te whārite. I roto i te ahupūngao me te pāngarau, he mea nui te mārama ki te tāpiri i ngā whārite e rua hei whakaoti rapanga. He maha ngā tikanga hei tāpiri i ngā whārite, ko tētahi o ēnei ko te tikanga tapatoru. I roto i tēnei tuhinga, ka matapakihia e mātou ngā tauira me te tāpiri i ngā whārite e rua mā te whakamahi i te tikanga tapatoru.
Tikanga Tapatoru i roto i te Tāpiritanga Wetere
I mua i te urunga atu ki te tauira rapanga, me mārama tātou ki te whakamahinga o te tikanga tapatoru hei tāpiri i ngā whārite e rua. Ko ngā mahi o te tikanga tapatoru e whai ake nei:
1. Te Whakatakoto i ngā Wētera e Rua ki tētahi Pūwāhi Kotahi: Ka whakanohoia te wētera tuatahi kia takoto tōna hiku (tīmatanga) ki te pūwāhi tīmatanga kua whiriwhiria.
2. Te Whakaahua i te Wēkita Tuarua: Ka tāpirihia te wēkita tuarua ki te pito (te pūwāhi mutunga) o te wēkita tuatahi.
3. Te Whakatau i te Wēka Hua: Ko te wēka hua ko te wēka e hono ana i te tīmatanga o te wēka tuatahi ki te mutunga o te wēka tuarua.
Tohu Wēka
Mō ngā kaupapa o tēnei tuhinga, ka whakamahia e mātou te tuhipoka vector penei:
– Ngā tohu tāpua kua tuhia ki te momotuhi matotoru, me te pere rānei kei runga (hei tauira, A, \(\vec{A}\) rānei).
– Ko ngā wāhanga whārite i roto i ngā ahunga \(x\) me \(y\) kua tuhia ki te āhua \(A_x\) me \(A_y\) mō te whārite \(\vec{A}\).
Tauira raruraru
Nā, me titiro tātou ki tētahi tauira rapanga hei āwhina i a tātou ki te mārama ki te tāpiri i ngā whārite e rua mā te whakamahi i te tikanga tapatoru.
Pātai:
E rua ngā whārite A me B e hoatu ana penei:
– E 4 ngā waeine te rahi o te whārite A, ā, e 30 nekehanga te ahunga ki te raki-mā-rāwhiti.
– E 3 ngā waeine te rahi o te whārite B, ā, e 60 ngā nekehanga te ahunga ki te raki-mā-rāwhiti.
Tātaihia te hua o te whārite R mai i te tāpiritanga o ngā whārite e rua mā te whakamahi i te tikanga tapatoru.
Kōrero
Hipanga 1: Te Tuhi i ngā Wētera
Tuatahi, ka tuhia e tātou te whārite A me te rahi o ngā waeine e 4 me te ahunga o te 30 nekehanga ki te raki-mā-rāwhiti. Kātahi, mai i te pito o te whārite A, ka tuhia e tātou te whārite B me te rahi o ngā waeine e 3 me te ahunga o te 60 nekehanga ki te raki-mā-rāwhiti.
Hipanga 2: Te Tatau i ngā Wāhanga Wetereo
Muri iho, ka tatauhia e mātou ngā wāhanga o ia whārite i ngā ahunga \(x\) me \(y\).
Ngā wāhanga o te whārite \(\vec{A}\):
\[
A_x = A \cos \theta_1 = 4 \cos 30^\circ = 4 \times \frac{\sqrt{3}}{2} = 2\sqrt{3}
\]
\[
A_y = A \sin \theta_1 = 4 \sin 30^\circ = 4 \times \frac{1}{2} = 2
\]
Ngā wāhanga o te pūwero \(\vec{B}\):
\[
B_x = B \cos \theta_2 = 3 \cos 60^\circ = 3 \times \frac{1}{2} = 1.5
\]
\[
B_y = B \sin \theta_2 = 3 \sin 60^\circ = 3 \times \frac{\sqrt{3}}{2} = 1.5\sqrt{3}
\]
Hipanga 3: Te Tāpiri i ngā Wāhanga Vector
Ka tāpirihia e mātou ngā wāhanga o ngā whārite e rua hei tiki i ngā wāhanga o te whārite hua \(\vec{R}\).
\[
R_x = A_x + B_x = 2\sqrt{3} + 1.5
\]
\[
R_y = A_y + B_y = 2 + 1.5\sqrt{3}
\]
Hipanga 4: Tātaihia te Rahi me te Aronga o te Wētera Hua
Ka tatauhia te rahi o te whārite hua \(\vec{R}\) mā te whakamahi i te ariā Pythagorean:
\[
R = \sqrt{R_x^2 + R_y^2}
\]
\[
R_x = 2\sqrt{3} + 1.5 \approx 3.464 + 1.5 = 4.964
\]
\[
R_y = 2 + 1.5\sqrt{3} \approx 2 + 2.598 = 4.598
\]
\[
R = \sqrt{(4.964)^2 + (4.598)^2} \approx \sqrt{24.640 + 21.145} \approx \sqrt{45.785} \approx 6.75 \text{ ngā waeine}
\]
Ka tatauhia te ahunga o te whārite hua \(\vec{R}\) mā te whakamahi i te mahi pātōtō-ira:
\[
\tan \phi = \frac{R_y}{R_x} = \frac{4.598}{4.964} \approx 0.926
\]
\[
\phi = \tan^{-1}(0.926) \approx 42.6^\circ \text{ mai i te raki mā rāwhiti}
\]
Whakamutunga
Mai i ngā hua o runga ake nei, ka taea e tātou te whakatau ko te rahi o te whārite \(\vec{R}\) mai i te tāpiritanga o ngā whārite \(\vec{A}\) me \(\vec{B}\) mā te whakamahi i te tikanga tapatoru he tata ki te 6.75 ngā waeine me te ahunga o te 42.6 nekehanga mai i te raki-mā-rāwhiti.
Te Katinga
He tikanga tino whai hua te tāpiri i ngā whārite e rua mā te whakamahi i te tikanga tapatoru e whakamahia whānuitia ana i roto i te ahupūngao me te hangarau. Mā te tuhi i ngā whārite me te tāpiri i ō rātou wāhanga, ka taea e tātou te kimi ngāwari i te whārite hua. Ko te tumanako, kua āwhina tēnei tuhinga i a koe ki te mārama ki te ariā o te tāpiri whārite mā te whakamahi i te tikanga tapatoru, ā, ka taea te whakamahi ki ngā raruraru maha e pā ana ki a koe i roto i ō akoranga.
