Isibonelo sombuzo wokuthola indawo yento ehambayo ku-parabola

Izibonelo ezintathu zemibuzo mayelana nokunquma indawo yento ehambayo ku-parabola

1. Ibhola liphonswa phezulu nge-engeli engu-60^o ngokuvundlile ngesivinini sokuqala esingu-12 m/s. Thola indawo yento ngemva kokuhamba umzuzwana owodwa! Ukusheshisa kwamandla adonsela phansi = 10m/s²
Ingxoxo
Kuyaziwa ukuthi:
I-engeli (θ) = 60^o
I-Kecepatan isiqalo (v)_o) = 12 m/s
Isikhawu sesikhathi (t) = 1 imizuzwana
Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s²
Kubuziwe: Indawo yebhola ngemva kokuhamba umzuzwana owodwa
Impendulo:
Okokuqala bala izingxenye zejubane lokuqala lebhola eziqondisweni ezivundlile neziqondile.
Ijubane lokuqala lebhola ohlangothini oluvundlile:
v_ox =v_o cos θ = (12 m/s)(cos 60^o) = (12 m/s)(0,5) = 6 m/s

Ijubane lokuqala lebhola ohlangothini oluqondile:
v_oy =v_o isono θ = (12 m/s)(isono 60^o) = (12 m/s)(0,5√3) = 6√3 m/s

Ukunyakaza kwe-parabolic kubhekwa njengenhlanganisela yokunyakaza okuvundlile nokuqondile. Ukunyakaza okuvundlile kuhlaziywa kanje: ukunyakaza okuqondile okufanayo, kuyilapho ukunyakaza ohlangothini oluqondile kuhlaziywa njengoba ukunyakaza okuqonde phezulu. Indawo yento eqonde ngqo ibalwa njengokunquma ibanga lento ehamba emgqeni oqondile ngesivinini esingaguquki, ngokuphambene nalokho indawo yento eqonde ngqo ibalwa njengokunquma ukuphakama kwento ehamba phezulu ngokuqondile.

Indawo yebhola ohlangothini oluvundlile:
Kuyaziwa ukuthi:
Isivinini sebhola ohlangothini oluvundlile (v_x) = 6 m/s
Ngokunyakaza okuqondile okufanayo, ijubane lento lihlala linjalo ukuze ijubane lokuqala lento lifane nejubane lento.
Isikhawu sesikhathi (t) = 1 imizuzwana
Kubuziwe: Ibanga lezinto
Impendulo:
Ijubane lamamitha ayi-6 ngomzuzwana lisho ukuthi ibhola lihamba amamitha ayi-6 ngomzuzwana. Ibanga elihanjwa yibhola ngemva komzuzwana owodwa lingamamitha ayi-6. Ngakho-ke, indawo evundlile yebhola ingamamitha ayi-6.

Indawo yebhola ohlangothini oluqondile:
Ekuxazululeni inkinga yokunyakaza okuqonde phezulu, ubuningi bevektha Ivektha ebheke phezulu inikezwa uphawu oluhle, ivektha ebheke phansi inikezwa uphawu olubi.
Kuyaziwa ukuthi:
Ijubane lokuqala lebhola (v)_o) = 6√3 m/s (kuhle ngoba isiqondiso sejubane lokuqala siphezulu)
Isikhawu sesikhathi (t) = 1 imizuzwana
Ukusheshisa ngenxa yamandla adonsela phansi (g) = -10 m/s² (okungekuhle ngoba ukusheshisa kwamandla adonsela phansi kuya phansi maphakathi nomhlaba)
Kubuziwe: Ukuphakama kwebhola ngemva kokuhamba umzuzwana owodwa (h)
Impendulo:
Kuyaziwa ukuthi v_o, t, g bese ubuza u-h ngakho ifomula esetshenzisiwe ithi h = v_o t + 1/2 gt²
h = v_o t + 1/2 gt² = (6√3)(1) + 1/2 (-10)(1²) = 6√3 + (-5)(1) = 6√3 – 5 = 6(1,7) – 5 = 10,2 – 5 = 5,2 amamitha.

Indawo yebhola ngemva kokuhamba umzuzwana owodwa:
Indawo yebhola ohlangothini oluvundlile (x) = amamitha ayi-6
Indawo yebhola ohlangothini oluqondile (y) = 5,2 amamitha
Ngakho-ke izixhumanisi zesikhundla sebhola ziyi-(x; y) = (6; 5,2)

2. Inhlamvu idutshulwe phezulu nge-engeli engu-30°^o ngokuvundlile ukusuka endaweni engamamitha angama-20 ngaphezu komhlabathi. Ijubane lokuqala lenhlamvu lingama-50 m/s. Inhlamvu izofinyelela phezulu kangakanani ngemva kokuhamba umzuzwana owodwa? Ukusheshisa okubangelwa amandla adonsela phansi kungama-10 m/s²
Ingxoxo
Kuyaziwa ukuthi:
I-engeli (θ) = 30^o
Ukuphakama kokuqala kwenhlamvu (h_o) = 20 amamitha
Ijubane lokuqala lenhlamvu (v)_o) = 50 m/s
Isikhawu sesikhathi (t) = 1 imizuzwana
Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s²
Kubuziwe: Ukuphakama kwenhlamvu
Impendulo:
Ijubane lokuqala lenhlamvu ohlangothini oluqondile:
Okokuqala bala ingxenye yokuqala yejubane lebhola ohlangothini oluqondile.
v_oy =v_o isono θ = (50 m/s)(isono 30^o) = (50 m/s)(0,5) = 25 m/s

Ukuphakama kwenhlamvu:
Ukuphakama kwenhlamvu kubalwa njengokunquma ukuphakama ngokunyakaza okuqonde phezulu.
Ekuxazululeni izinkinga zokunyakaza okuqonde phezulu, inani levektha eliqondiswe phezulu linikezwa uphawu oluhle, inani levektha eliqondiswe phansi linikezwa uphawu olubi.
Kuyaziwa ukuthi:
Ijubane lokuqala lenhlamvu (v)_o) = 25 m/s (kuhle ngoba isiqondiso sejubane lokuqala siphezulu)
Isikhawu sesikhathi (t) = 1 imizuzwana
Ukusheshisa ngenxa yamandla adonsela phansi (g) = -10 m/s² (okungekuhle ngoba isiqondiso sokusheshisa kwamandla adonsela phansi sibheke enkabeni yomhlaba)
Kubuziwe: Ukuphakama kwenhlamvu (h)
Impendulo:
Kuyaziwa ukuthi v_o, t, g bese ubuza u-h ngakho ifomula esetshenzisiwe ithi h = v_o t + 1/2 gt²
h = v_o t + 1/2 gt² = (25)(1) + 1/2 (-10)(1)²) = 25 + (-5)(1) = 25 – 5 = amamitha angu-20.
Ukuphakama kwenhlamvu ngemva kokuhamba umzuzwana owodwa kungamamitha angama-20 ngaphezu kwalapho inhlamvu idutshulwe khona noma amamitha angama-40 ngaphezu komhlabathi.

3. Imabula iphonswa ngokuvundlile ngakwesokudla isuka ekuphakameni kwamamitha ayi-10 ngesivinini sokuqala esingu-10 m/s. Nquma indawo yemabula ngemva kokuhamba umzuzwana owodwa! Ukusheshisa ngenxa yamandla adonsela phansi = 10 m/s²
Ingxoxo
Kuyaziwa ukuthi:
Ukuphakama kokuqala (h) = amamitha ayi-10
Ijubane lokuqala (v)_o) = 10 m/s
Isikhawu sesikhathi (t) = 1 imizuzwana
Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s²
Kubuziwe: Indawo yemabula ngemva kokuhamba umzuzwana owodwa
Impendulo:
Indlela yemabula injengoba kuboniswe esithombeni. Uma indlela ifana neyomfanekiso njengoba kuboniswe esithombeni, indawo yento ohlangothini oluqondile inqunywa njengokubala ukuphakama ekuwa okukhululekile, kuyilapho indawo yento ohlangothini oluqondile inqunywa njengokubala ibanga ngokunyakaza okuqondile okufanayo.
Ekuqaleni imabula ihamba ngendlela evundlile ukuze ijubane lokuqala lemabula libe ngendlela evundlile (v)._ox) ingu-10 m/s, kuyilapho ijubane lokuqala lemabula liqonde ngqo (v_oy) ngu-0 m/s.

Indawo yamamabula ohlangothini oluvundlile:
Kuyaziwa ukuthi:
Isivinini semabula ohlangothini oluvundlile (v)_x) = 10 m/s
Ngokunyakaza okuqondile okufanayo, ijubane lento lihlala linjalo ukuze ijubane lokuqala lento lifane nejubane lento.
Isikhawu sesikhathi (t) = 1 imizuzwana
Kubuziwe: Ibanga lezinto
Impendulo:
Ijubane lamamitha ayi-10 ngomzuzwana lisho ukuthi imabula ihamba amamitha ayi-10 ngomzuzwana. Ibanga elihanjwa imabula ngemva kokuhamba umzuzwana owodwa lingamamitha ayi-10. Ngakho-ke, indawo evundlile yemabula ingamamitha ayi-10.

Indawo yamamabula ohlangothini oluqondile:
Kuhlaziywe njenge ukunyakaza kokuwa kwamahhala.
Kuyaziwa ukuthi:
Isikhawu sesikhathi (t) = 1 imizuzwana
Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s²
Kubuziwe: Ukuphakama kwemabula ngemva kokuhamba umzuzwana owodwa (h)
Impendulo:
Njengoba kunikezwe u-t, u-g bese kucelwe u-h ngakho ifomula esetshenzisiwe ingu-h = 1/2 gt²
h = 1/2 gt² = 1/2 (10)(1²) = (5)(1) = amamitha ama-5.
Ngemva komzuzwana owodwa, imabula iwela ngamamitha angu-5. Ukuphakama kwemabula ngaphezu komhlaba kungamamitha ayi-10 - amamitha angu-5 = amamitha angu-5.

Indawo yemabula ngemva kokuhamba umzuzwana owodwa:
Indawo yemabula ohlangothini oluvundlile (x) = amamitha ayi-10
Indawo yemabula ohlangothini oluqondile (y) = amamitha angu-5
Ngakho-ke izixhumanisi zesikhundla semabula ziyi-(x; y) = (10; 5)

[IsiNgisi: Ukuxazulula izinkinga zokunyakaza okubonakalayo - ukunquma indawo yento]