27 Ukunyakaza okuneziqhumane - izinkinga nezixazululo
1. Inhlamvu idutshulwa nge -engeli engu -θ = 60 o ngesivinini esingu- 20 m/s. Ukusheshisa ngenxa yamandla adonsela phansi kungu- 10 m/s 2 . Yisiphi isikhathi esinqunyiwe ukuze kufinyelelwe ukuphakama okuphezulu?
Kwaziwa:
Ijubane lokuqala lenhlamvu (v o ) = 20 m/s
I-engeli (θ) = 60 o C
Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 ms –2
Okufunwayo: Isikhathi sokufinyelela ukuphakama okuphezulu
Isixazululo:
Ijubane lokuqala ohlangothini oluvundlile (x axis):
v inkabi = v o cos 60 o = (20) (0.5) = 10 m/s
Ijubane lokuqala esiqondisweni esiqondile (i-y axis):
v oy = vo isono 60 o = (20)(0.5√3) = 10√3 m/s
Isikhathi sokufinyelela ukuphakama okuphezulu, sibalwa kusetshenziswa lesi sibalo:
v ty = v oy + gt
v ty = ijubane lokugcina ohlangothini oluqondile = ijubane lokugcina endaweni ephakeme kakhulu = 0 m/s
v oy = ijubane lokuqala endaweni evundlile = 10√3 m/s
g = ukusheshisa ngenxa yamandla adonsela phansi = 10 m/s 2
t = isikhawu sesikhathi
Isikhawu sesikhathi:
v ty = v oy + gt
0 = 10√3 – 10 t
10√3 = 10 t
t = 10√3 / 10
t = √3 imizuzwana
2. Into evezwe nge-engeli. Ukuphakama kwento kuyafana uma isikhathi sesikhawu = umzuzwana o-1 kanye nemizuzwana emi-3. Iyini isikhathi sesikhawu sento esemoyeni.
Isixazululo:
Into isemoyeni imizuzwana emi-4.
3. Indiza ihamba ngokuvundlile ngesivinini esingama-50 m/s. Ekuphakameni kwamakhilomitha ama-2, into iyawa endizeni. Ukusheshisa ngenxa yamandla adonsela phansi = 10 m/ s2, yisiphi isikhathi esinqunyiwe ngaphambi kokuba into ishaye phansi.
Kwaziwa:
Ukuphakama = 2 km = amamitha angu-2000
Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s 2
Okufunwayo: Isikhathi esiphakathi (t)
Isixazululo:
h = 1/2 gt 2
2000 = 1/2 (10) t 2
2000 = 5 t 2
t 2 = 2000/5 = 400
t = √400 = imizuzwana engama-20
4. Ibhola elikhahlelwayo lishiya umhlabathi nge-engeli engu-θ = 45 o kanti elivundlile linesivinini sokuqala esingu-25 m/s. Nquma ibanga lika-X. Ukusheshisa ngenxa yamandla adonsela phansi kungu-10 m/s 2.
Kwaziwa:
Isivinini sokuqala (v o ) = 25 m/s
Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s 2
I-engeli (θ) = 45 o
Kufunwa: X
Isixazululo:
Ingxenye evundlile yejubane lokuqala:
v inkabi = v o cos θ = (25 m/s)(cos 45 o ) = (25 m/s)(0.5√2) = 12.5√2 m/s
Ingxenye eqondile yejubane lokuqala:
v oy = v o isono θ = (25 m/s)(isono 45 o ) = (25 m/s)(0.5√2) = 12.5√2 m/s
Ukunyakaza okubonakalayo kungaqondwa ngokuhlaziya izingxenye ezivundlile neziqondile zokunyakaza ngokwehlukana. Ukunyakaza kuka-x kwenzeka ngesivinini esingaguquki kanti ukunyakaza kuka-y kwenzeka ngokusheshisa okungaguquki kwamandla adonsela phansi.
Isikhathi emoyeni (t):
Isikhathi emoyeni sibalwa ngesibalo sokunyakaza okuqonde phezulu.
Khetha indlela eya phezulu njengeyakhayo kanye nendlela eya phansi njengeyakhayo.
Kwaziwa:
Ijubane lokuqala (v o ) = 12.5√2 m/s (isiqondiso esibheke phezulu, esihle)
Ukusheshisa ngenxa yamandla adonsela phansi (g) = -10 m/s 2 (isiqondiso esiya phansi, esingesihle)
Ukuphakama (h) = 0
Okufunwayo: Isikhathi esiphakathi (t)
Isixazululo:
h = vot + 1/2 gt 2
0 = (12.5√2) t + 1/2 (-10) t 2
0 = 12.5√2 t – 5 t 2
12.5√2 t = 5 t 2
12.5√2 = 5 t
t = 12.5√2 / 5
t = 2.5√2 imizuzwana
Ibanga elivundlile (X):
Kubalwa kusetshenziswa isibalo sokunyakaza okuqondile okufanayo ngejubane elingaguquki.
Kwaziwa:
Ijubane (v) = 12.5√2 m/s
Isikhawu sesikhathi (t) = 2.5√2 imizuzwana
Okufunwayo: Ibanga
Isixazululo:
d = vt = (12.5√2)(2.5√2) = (12.5)(2.5)(2) = amamitha angu-62.5
5. Into ephakanyisiwe phezulu nge-engeli engu-θ = 30 o ene-horizontal inesivinini sokuqala esingu-20 m/s. Ukusheshisa ngenxa yamandla adonsela phansi kungu-10 m/s 2 . Nquma ukuphakama okuphezulu.
Kwaziwa:
Ijubane lokuqala (v)o) = 20 m/s
Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s 2
I-engeli (θ) = 30 o
Okufunwayo : Ukuphakama okuphezulu
Isixazululo:
Okokuqala, thola ingxenye eqondile yejubane lokuqala (v oy ):
v oy = v o isono 30 o = (20)(isono 30 o ) = (20)(0.5) = 10 m/s
Bala ukuphakama okuphezulu. Khetha isiqondiso esibheke phezulu njengesihle kanye nesiqondiso esibheke phansi njengesibi.
Kwaziwa:
Ukusheshisa ngenxa yamandla adonsela phansi (g) = -10 m/s 2 ( isiqondiso esiya phansi , esingesihle )
Ingxenye eqondile yejubane lokuqala (v oy ) = 10 m/s ( isiqondiso esibheke phezulu, esihle )
Ijubane ekuphakameni okuphezulu (v ty ) = 0
Okufunwayo: Ukuphakama okuphezulu (h)
Isixazululo:
v t 2 = v o 2 + 2 gh
0 2 = 10 2 + 2 (-10) h
0 = 100 – 20 amahora
100 = amahora angu-20
h = 100/20
h = amamitha angu-5
Ukuphakama okuphezulu kungamamitha ama-5.
6. Into iphonswa nge-engeli ethile yokuphakama. Ukuphakama kwento kuyafana ngemva komzuzwana owodwa kanye nemizuzwana emi-3. Thola isikhathi emoyeni.
A. 3.6 imizuzwana
B. 4.0 imizuzwana
C. 5.6 imizuzwana
D. 6.4 imizuzwana
Isixazululo
Isikhathi emoyeni = imizuzwana emi-4.
Impendulo efanele ngu-B.
7. Indiza ihamba ngokuvundlile ngesivinini esingama-50 m/s. Uma indiza iphakeme ngamakhilomitha ama-2, into ingawa ngokukhululeka endizeni. Thola uhlobo lokunyakaza.
A. Ukunyakaza kokuwa okukhululekile
B. Ukunyakaza okuntantayo
C. Ukunyakaza okuvundlile
D. Ukunyakaza okuneziqhumane
Isixazululo:
Into iwiswa endizeni ehambayo ngoba inejubane elifanayo nelendiza, okungu-50 m/s. Ukunyakaza kwezinto akufani nokunyakaza kokuwa ngokukhululeka kodwa ukunyakaza okufana nokwe-parabolic. Icala lifana nokuthi uwisa izinto ngaphakathi emotweni ehambayo.
Impendulo efanele ngu-D.
8. Ibhola liphonswa ngokuvundlile ngesivinini esingamamitha ayi-15/s lisuka edwaleni elingamamitha angama-60 ukuphakama. Kuthatha isikhathi esingakanani ukushayisa phansi?
Isixazululo: Sisebenzisa i-\( h = \frac{1}{2} gt^2 \), sithola ukuthi isikhathi singu-\( t = \sqrt{\frac{2h}{g}} \approx 3.5\ \text{s} \).
9. Isibhamu sidubula nge-engeli engu-30° ngaphezu kwendawo evundlile ngesivinini sokuqala esingu-20 m/s. Kungakanani ukuphakama okuphezulu okufinyelelwe?
Isixazululo: Ukusebenzisa i-\( h = \frac{v^2 \sin^2 \theta}{2g} \), ukuphakama okuphezulu kungu-\( h \approx 10.2\ \text{m} \).
10. Itshe liphonswa ngokuvundlile ngesivinini esingamamitha ayi-10/s ukusuka embhoshongweni ongamamitha angama-80 ubude. Thola ibanga elivundlile elihambayo ngaphambi kokushayisa phansi.
Isixazululo: Ukusebenzisa isikhathi esitholakala ngendlela efanayo neNkinga 1, ibanga elivundlile lingu-\( d = vt \approx 40\ \text{m} \).
11. Ibhola lenganono lidutshulwe ku-40 m/s nge-engeli engu-45°. Thola isikhathi sokundiza.
Isixazululo: Ukusebenzisa i-\( t = \frac{2v \sin \theta}{g} \), isikhathi sokundiza yi-\( t \approx 5.8\ \text{s} \).
12. Ibhola lezinyawo liphonswa nge-engeli engu-60° ngesivinini esingu-12 m/s. Thola ibanga elivundlile.
Isixazululo: Ukusebenzisa i-\( R = \frac{v^2 \sin 2\theta}{g} \), ububanzi bungu-\( R \approx 14.0\ \text{m} \).
13. I-projectile ikhishwa ngesivinini sokuqala esingu-50 m/s ku-37° ngaphezu kwendawo evundlile. Iyini ingxenye yesivinini esivundlile?
Isixazululo: Ingxenye eqondile ingu-\( v_y = v \sin \theta \approx 30\ \text{m/s} \).
14. Isibhamu siqhunyiswa ngokuvundlile ngesivinini esingama-20 m/s ukusuka ekuphakameni kwamamitha ayi-100. Ingakanani ijubane eliqondile ngaphambi nje kokuba lishaye phansi?
Isixazululo: Ukusebenzisa i-\( v_y = \sqrt{2gh} \), ijubane eliqondile lingu-\( v_y \approx 44.7\ \text{m/s} \).
15. Itshe liphonswa nge-engeli engu-25° ngaphezu kwendawo evundlile ngesivinini sokuqala esingu-15 m/s. Yiziphi izingxenye ezivundlile nezivundlile zejubane?
Isixazululo: Ingxenye evundlile ingu-\( v_x = v \cos \theta \approx 13.4\ \text{m/s} \), kanti ingxenye evundlile ingu-\( v_y \approx 6.4\ \text{m/s} \).
16. Ibhola lezinyawo likhahlelwa ngesivinini sokuqala esingu-30 m/s nge-engela engu-40° ngaphezu kwe-horizontal. Iyini ingxenye yalo yejubane elivundlile?
Isixazululo: Ingxenye evundlile ingu-\( v_x = v \cos \theta \approx 22.9\ \text{m/s} \).
17. Ibhola legalofu lishaywa ngesivinini sokuqala esingu-70 m/s nge-engeli engu-20°. Isikhathi sokundiza singakanani?
Isixazululo: Ukusebenzisa isikhathi se-equation yendiza, isikhathi singu-\( t \approx 4.9\ \text{s} \).
18. Isibhamu esidubulayo sidubula phansi ngesivinini esingama-25 m/s ku-53° ngaphezu kwendawo evundlile. Iyini ingxenye yaso yokuqala yejubane eliqondile?
Isixazululo: Ingxenye eqondile ingu-\( v_y = v \sin \theta \approx 20\ \text{m/s} \).
19. Ibhola lezinyawo liphonswa ngesivinini sokuqala esingu-20 m/s nge-engeli engu-50°. Kuyini ukuphakama okuphezulu?
Isixazululo: Ukusebenzisa i-equation yokuphakama okuphezulu, ukuphakama kungu-\( h \approx 15.3\ \text{m} \).
20. Inhlamvu idutshulwa ngokuvundlile ngesivinini esingama-200 m/s ukusuka ekuphakameni kwamamitha ayi-10. Kuthatha isikhathi esingakanani ukushaya phansi?
Isixazululo: Ukusebenzisa i-equation yesikhathi, isikhathi singu-\( t \approx 1.4\ \text{s} \).
21. Ibhola le-cannon lidutshulwe ku-45 m/s nge-engeli engu-30°. Thola ibanga.
Isixazululo: Ukusebenzisa i-range equation, i-range ingu-\( R \approx 88.2\ \text{m} \).
22. Ibhola lomnqakiswano liphonswa nge-engeli engu-75° ngesivinini esingu-10 m/s. Thola ibanga elivundlile.
Isixazululo: Ukusebenzisa i-range equation, i-range ingu-\( R \approx 5.3\ \text{m} \).
23. I-projectile ikhishwa ngesivinini sokuqala esingu-30 m/s ku-22° ngaphezu kwendawo evundlile. Ingakanani ijubane eliqondile ngaphambi nje kokuba ishaye phansi?
Isixazululo: Ukusebenzisa i-equation ye-vertical velocity, i-vertical velocity ingu-\( v_y \approx 11.4\ \text{m/s} \).
24. Itshe liphonswa ngokuvundlile ngamamitha angu-8/s ukusuka embhoshongweni ongamamitha angu-40 ubude. Lingakanani ibanga elivundlile elilihambayo?
Isixazululo: Ukusebenzisa i-equation yebanga elivundlile, ibanga lingu-\( d \approx 16\ \text{m} \).
25. Ibhola lezinyawo likhahlelwa ngesivinini sokuqala esingu-12 m/s nge-engela engu-30° ngaphezu kwe-horizontal. Yiziphi izingxenye zejubane ezivundlile neziqondile?
Isixazululo: Ingxenye evundlile ingu-\( v_x \approx 10.4\ \text{m/s} \), kanti ingxenye evundlile ingu-\( v_y \approx 6\ \text{m/s} \).
26. Ibhola legalofu lishaywa ngesivinini sokuqala esingu-50 m/s nge-engeli engu-15°. Isikhathi sokundiza singakanani?
Isixazululo: Ukusebenzisa isikhathi se-equation yendiza, isikhathi singu-\( t \approx 2.6\ \text{s} \).
27. Isibhamu esidubulayo sidubula phansi ngesivinini esingama-40 m/s ku-60° ngaphezu kwesivundlile. Iyini ingxenye yaso yokuqala yejubane elivundlile?
Isixazululo: Ingxenye evundlile ingu-\( v_x = v \cos \theta \approx 20\ \text{m/s} \).
