3 mau laʻana o nā nīnau neʻe kū i luna
1. Hoʻolei ʻia ka pōpō i luna me ka wikiwiki mua o 20 m/s. E hoʻoholo i ke kiʻekiʻe loa o ka pōpō. g = 10 m/s2
Pahana
I ka neʻe ʻana i luna, ke neʻe i luna kahi mea, e emi ana kona wikiwiki, a ke neʻe hou i lalo, e wikiwiki ana. No laila, ʻo ka neʻe ʻana i luna he laʻana nō hoʻi ia o GLBB.
Formula GLBB :
vt = vo + ma
s = vo t + ½ ma2
vt2 = vo2 + 2 mau ʻauamo
Ua hoʻololi ʻia ke ʻano GLBB ma luna a ua hoʻoponopono ʻia i nā kūlana o ka neʻe ʻana i luna, me kekahi mau nota.
Haʻilula Neʻe Kū i luna :
vt = vo + gt
h = vo t + ½ gt2
vt2 = vo2 + 2 gh
Wehewehe: vt = ka wikiwiki hope loa, vo = ka wikiwiki mua, g = ka wikiwiki ma muli o ke koʻikoʻi, t = ka wā manawa, h = ke kiʻekiʻe.
Catatan:
Ka mua, i ka hoʻoponopono ʻana i nā pilikia o ka neʻe ʻana i luna, hāʻawi ʻia ka nui vector i kuhikuhi ʻia i luna i kahi hōʻailona maikaʻi, hāʻawi ʻia ka nui vector i kuhikuhi ʻia i lalo i kahi hōʻailona maikaʻi ʻole.
Ka lua, inā ʻoi aku ke kūlana hope o ka mea ma mua o ke kūlana mua (ʻo ke kūlana mua ke kiko kuhikuhi) a laila maikaʻi ka neʻe ʻana (h) o ka mea. I ka ʻaoʻao ʻē aʻe, inā ʻoi aku ka kūlana hope ma mua o ke kūlana mua a laila maikaʻi ʻole ka neʻe ʻana o ka mea.
Ke kolu, ma ke kiʻekiʻe loa, ua noho mālie ka mea no kekahi manawa ma mua o ka hoʻololi ʻana i ke kuhikuhi, no laila ka wikiwiki o ka mea = 0.
Ua ʻike ʻia:
vo = 20 m/s (maikaʻi no ka mea ʻo ke kuhikuhi o ka wikiwiki mua i luna = ua kiola ʻia ka mea i luna), g = – 10 m/s2 (maikaʻi ʻole no ka mea ʻo ke kuhikuhi o ka wikiwiki o ka umekaumaha e iho mau ana i lalo, vt = 0 (ma ke kiʻekiʻe loa, ua hoʻomaha ka mea no kekahi manawa)
Ua nīnau ʻia:
Kiʻekiʻe loa (h) ?
Pane:
2. Ua kiola ʻia kekahi kinikini i luna mai kahi hale he 100 mika ma luna o ka honua me ka wikiwiki mua o 20 m/s. E hoʻoholo (a) i ka manawa e pono ai e hiki i ka honua (b) i ka wikiwiki o ke kinikini i kona hiki ʻana i ka honua. g = 10 m/s2
Pahana
Ua ʻike ʻia:
h = -100 mika
vo = 20m/s
g = -10 m/s2
Ua nīnau ʻia:
(a) ka manawa manawa (t)
(b) ka wikiwiki hope loa (vt)
Pane:
(a) ka manawa manawa (t)
Hāʻawi ʻia ʻo h = -100 mika (maikaʻi ʻole no ka mea aia ke kūlana hope loa o ke kinikini ma lalo o ke kūlana mua o ke kinikini), vo = 20 m/s (maikaʻi no ka mea ʻo ke kuhikuhi o ka wikiwiki mua i luna a i ʻole ke kuhikuhi o ka neʻe mua i luna), g = -10 m/s2 (maikaʻi ʻole no ka mea, ʻo ke kuhikuhi o ka wikiwiki o ka umekaumaha e iho ana i lalo).
ʻAʻole hiki i ka manawa ke loaʻa kahi waiwai maikaʻi ʻole, no laila hoʻohana ʻia ʻo t.2 = 6,9 kekona.
(b) Ka wikiwiki hope loa
Hāʻawi ʻia ʻo h, vo a me g, ua nīnau ʻia ʻo vt, no laila e hoʻohana i ke ʻano haʻilula ʻekolu.
3. Ua kiola ʻia ka pōpō A i luna me ka wikiwiki o 10 ms -1 . Hoʻokahi kekona ma hope mai, mai ke kiko like, ua kiola ʻia ka pōpō B i luna ma ke ala like me ka wikiwiki o 25 ms -1 . ʻO ke kiʻekiʻe i hiki i ka pōpō B ke hālāwai me ka pōpō A ʻo...
A. 0,20 m
B. 4,80 m
C. 5,00 m
D. 5,20 m
E. 31,25 m
Pahana
I ka hoʻoponopono ʻana i nā pilikia ma ka neʻe ʻana i luna , hāʻawi ʻia ka nui vector i kuhikuhi ʻia i luna i kahi hōʻailona maikaʻi, hāʻawi ʻia ka nui vector i kuhikuhi ʻia i lalo i kahi hōʻailona maikaʻi ʻole.
Ua ʻike ʻia:
Ka wikiwiki mua (v o ) o ka pōpō A = 10 m/s
ʻO ka manawa (t) e kau ana ka pōpō A i ka lewa = x
Ka wikiwiki mua (v o ) o ka pōpō B = 25 m/s
ʻO ka manawa (t) e kau ana ka pōpō B i ka lewa = x – 1
Ka wikiwiki ma muli o ke koʻikoʻi (g) = -10 m/s 2 (ʻo ke kuhikuhi o ka wikiwiki ma muli o ke koʻikoʻi e iho ana i lalo no laila he hōʻailona maikaʻi ʻole kona)
Nīnau: ʻO ke kiʻekiʻe i hiki i ka pōpō B ke hālāwai me ka pōpō A (h)
ʻO nā nui i kēia manawa ʻo ia ka wikiwiki mua (v o ), ka wikiwiki o ka umekaumaha (g), ke kiʻekiʻe (h) a me ka manawa manawa (t) no laila ke ʻano i hoʻohana ʻia:
h = v o t + ½ gt 2
I mea e hālāwai ai, pono e like ke kiʻekiʻe o nā pōpō ʻelua.
h A = h B
v o t + ½ gt 2 = v o t + ½ gt 2
10x + ½ (-10) x 2 = 25 (x-1) + ½ (-10) (x-1) 2
10x – 5x 2 = 25 (x-1) – 5 (x-1) 2
10x – 5x 2 = 25x – 25 – 5 (x 2 -2x+1)
10x – 5x 2 = 25x – 25 – 5x 2 + 10x – 5
10x – 5x 2 – 25x + 25 + 5x 2 – 10x + 5 = 0
– 5x 2 + 5x 2 + 10x – 25x – 10x + 25 + 5 = 0
10x – 25x – 10x + 25 + 5 = 0
– 25x + 25 + 5 = 0
– 25x + 30 = 0
– 25x = – 30
x = -30/-25
x = 1,2 kekona
ʻO ka manawa i noho ai ka pōpō A i ka lewa ma mua o ka hālāwai ʻana me ka pōpō B = 1,2 kekona.
ʻO ka manawa e noho ai ka pōpō B i ka lewa ma mua o ka hālāwai ʻana me ka pōpō A = 1,2 kekona – 1 kekona = 0,2 kekona.
ʻO ke kiʻekiʻe i hiki i ka pōpō A ke hālāwai me ka pōpō B (h):
h = v o t + ½ gt 2 = (10)(1,2) + 1/2 (-10)(1,2) 2 = 12 – 5(1,44) = 12 – 7,2 = 4,8 mika
ʻO ke kiʻekiʻe i hiki i ka pōpō B ke hālāwai me ka pōpō A (h):
h = v o t + ½ gt 2 = (25)(0,2) + 1/2 (-10)(0,2) 2 = 5 – 5(0,04) = 5 – 0,2 = 4,8 mika
ʻO ka pane pololei ʻo B.
Nā nīnau e pili ana i ka neʻe ʻana i luna
1. Hoʻolei ʻia ka pōpō i luna me ka wikiwiki mua o 10 m/s. E hoʻoholo i ke kiʻekiʻe loa o ka pōpō. g = 10 m/s2
Pane:
h = 5 mika
2. Ua kiola ʻia kekahi kinikini i luna mai kahi hale he 50 mika ma luna o ka honua me ka wikiwiki mua o 5 m/s. E hoʻoholo (a) i ka manawa e pono ai e hiki i ka honua (b) i ka wikiwiki o ke kinikini i kona hiki ʻana i ka honua. g = 10 m/s2
Pane:
(a) t = 3,7 kekona (b) vt = 32m/s
[ʻŌlelo Pelekania: Neʻe ʻana i luna a i lalo i ka hāʻule manuahi - nā pilikia a me nā hoʻonā ]
