Nquma ukufuduka okuvundlile kokunyakaza kwe-projectile

Izinkinga ezixazululiwe ekuhambeni kwe-projectile - thola ukufuduka okuvundlile

1. Ibhola elikhahlelwayo lishiya phansi nge-engeli engu-θ = 60 ^o kanti elivundlile linejubane lokuqala elingu-16 m/s. Kuzoba isikhathi esingakanani ngaphambi kokuba ibhola lishaye phansi?

Kwaziwa:

I-engeli ( θ ) = 60 ^o

Isivinini sokuqala (v _o ) = 16 m/s

Ukusheshisa kwamandla adonsela phansi (g) = 10 m/s ²

Okufunwayo: Ukufuduka okuvundlile (x)

Isixazululo:

Ingxenye evundlile yejubane lokuqala:

v _inkabi = v _o cos θ = (16 m/s)(cos 60 ^o ) = (16 m/s)(0.5) = 8 m/s

Ingxenye eqondile yejubane lokuqala:

v _oy = v _o isono θ = (16 m/s)(isono 60 ^o ) = (16 m/s)(0.5 √ 3 ) = 8 √ 3 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

Isikhathi esihlala emoyeni sinqunywa ukunyakaza kuka-y. Siqala ngokuthola isikhathi sisebenzisa ukunyakaza kuka-y bese sisebenzisa leli nani lesikhathi kuzibalo zika-x ( isilinganiso sejubane esingaguquki ).

Khetha indlela eya phezulu njengeyakhayo kanye nendlela eya phansi njengeyakhayo.

Kwaziwa:

Ijubane lokuqala (v _o ) = 8 √ 3 m/s (v _o phezulu)

Ukusheshisa kwamandla adonsela phansi (g) = -10 m/s ² (g phansi)

Ukuphakama (h) = 0 (ibhola libuyele endaweni efanayo)

Kufunwa: Isikhathi Esisemoyeni

Isixazululo:

h = vot ₊ 1/2 gt ^{​​​​2}

0 = ( 8 √ 3) t + 1/2 (-10) t ²

0 = 8 √ 3 t – 5 t ²

8 √ 3 t = 5 t ²

8 (1.7) = 5 t

14 = 5 t

t = 14 / 5 = 2.8 imizuzwana

Ukufuduka okuvundlile

Kwaziwa:

Ijubane (v) = 8 m/s

Isikhawu sesikhathi (t) = imizuzwana eyi-2.8

Okufunwayo: Ukufuduka

Isixazululo:

x = vt = (8 m/s)(2.8 s) = 22.4 amamitha

Ukufuduka okuvundlile kungamamitha angu-22.4.

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2. Umzimba uphakanyiswa ubheke phezulu nge-engeli engu-60 ^o kanti ukuphakama kwawo kuqondile kusuka esakhiweni ngamamitha angu-50. Isivinini sawo sokuqala singama-30 m/s. Bala ukufuduka okuqondile! Ukusheshisa kwamandla adonsela phansi kungu-10 m/s ².

Kwaziwa:

I-engeli ( θ ) = 60 ^o

Ukuphakama (h) = 15 m

Isivinini sokuqala (v _o ) = 30 m/s

Ukusheshisa kwamandla adonsela phansi (g) = 10 m/s ²

Kufunwa: x

Isixazululo:

Ingxenye evundlile yejubane lokuqala ::

v _inkabi = v _o cos θ = (30 m/s)(cos 60 ^o ) = (30 m/s)(0.5) = 15 m/s

Ingxenye eqondile yejubane lokuqala:

v _oy = v _o isono θ = (30 m/s)(isono 60 ^o ) = (30 m/s)(0.5 √ 3 ) = 15 √ 3 m/s

Isikhathi emoyeni

Siqala ngokuthola isikhathi sisebenzisa ukunyakaza kuka-y bese sisebenzisa leli nani lesikhathi kuzibalo zika-x (isilinganiso sejubane eliqhubekayo). Khetha phezulu njengehle kanye nephansi njengehle.

Kwaziwa:

Ijubane lokuqala (v _o ) = 15 √ 3 m/s (elihle phezulu)

Ukusheshisa kwamandla adonsela phansi (g) = -10 m/s ² (ukwehla okungekuhle)

Ukuphakama (h) = -50 (Umhlaba ngamamitha angu-50 ngaphansi kwendawo yokuqala)

Kufunwa: t

Isixazululo:

h = vot ₊ 1/2 gt ^{​​​​2}

-50 = ( 15 √ 3 ) t + 1/2 (-10) t ²

-50 = 15 √ 3 t – 5 t ²

5 t ² – 15 √ 3 t – 50 = 0

Bala isikhathi usebenzisa le fomula:

a = 5, b = – 15 √ 3, c = – 50

Isikhathi emoyeni singamasekhondi angu-6.7.

Ukufuduka okuvundlile:

Kwaziwa:

Ijubane (v) = 15 m/s

Isikhawu sesikhathi (t) = imizuzwana eyi-6.7

Kufunwa: ukufuduka

Isixazululo:

s = vt = (15 m/s)(6.7 s) = amamitha ayi-100.5

Ukufuduka okuvundlile kungamamitha angu-100.5.

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3. Ibhola elincane liphakanyiswa ngokuvundlile ngesivinini sokuqala v _o = 10 m/s ukusuka esakhiweni esingamamitha ayi-10 ukuphakama. Bala ukufuduka okuvundlile ! Ukusheshisa kwamandla adonsela phansi kungu-10 m/s ²

Kwaziwa:

Ukuphakama (h) = 10 m

Ijubane lokuqala (v _o ) = 10 m/s

Ukusheshisa kwamandla adonsela phansi (g) = 10 m/s ²

Kufunwa: x

Isixazululo:

Ingxenye evundlile yejubane lokuqala = ijubane lokuqala = 10 m/s.

Isikhathi emoyeni

Isikhathi emoyeni sibalwa kusetshenziswa i-equation yokunyakaza kokuwa kwamahhala.

Kwaziwa:

Ukusheshisa kwamandla adonsela phansi (g) = 10 m/s ²

Ukuphakama (h) = amamitha ayi-10

Kufunwa: t

Isixazululo:

h = 1/2 gt ^{​​​​2}

10 = 1/2 (10) t ²

10 = 5 t ²

t ² = 10 / 5 = 2

t = √2 = 1.4 imizuzwana

Ukufuduka okuvundlile

Ukufuduka okuvundlile kubalwa kusetshenziswa i-equation yokunyakaza ngesivinini esingaguquki.

Kwaziwa:

Ijubane (v) = 10 m/s

Isikhawu sesikhathi (t) = imizuzwana eyi-1.4

Kufunwa: x

Isixazululo:

s = vt = (10 m/s)(1.4 s) = amamitha ayi-14

Ukufuduka okuvundlile kungamamitha angu-14.

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1. Xazulula ijubane lokuqala libe izingxenye ezivundlile neziqondile
2. Nquma ukufuduka okuvundlile
3. Nquma ukuphakama okuphezulu
4. Nquma isikhathi esinqunyiwe
5. Nquma indawo yezinto
6. Nquma ijubane lokugcina