Physics

1. Mpira wokankha umachoka pansi pa ngodya θ = 30 ^o kupita mopingasa ndi liwiro loyamba la 14 m/s. Werengani liwiro lomaliza mpira usanagwe pansi.

Zodziwika:

Ngodya ( θ ) = 3 0 ^o

Liwiro loyambirira (v _o ) = 14 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Akufuna: Liwiro lomaliza mpira usanagwe pansi

Yankho:

Gawo lolunjika la liwiro loyambirira:

v _ox = v _o cos θ = (14 m/s)(cos 30 ^o ) = (14 m/s) (0.5 √ 3 ) = 7 √ 3 m/s

Gawo loyima la liwiro loyambirira:

v _oy = v _o tchimo θ = (14 m/s) (tchimo 30 ^o ) = (14 m/s) (0.5) = 7 m/s

Liwiro lomaliza panjira yoyimirira

Sankhani njira yopita mmwamba ngati yabwino ndipo njira yopita pansi ngati yoipa.

Zodziwika:

Liwiro loyambirira (v _o ) = 7 m/s (zabwino mmwamba)

Kuthamanga kwa mphamvu yokoka (g) = – 10 m/s ² (yoyipa pansi)

Kutalika (h) = 0 (chinthu kubwerera ku malo oyamba)

Kufunidwa: Liwiro lomaliza (v _t )

Yankho:

v _t ² = v _o ² + 2 gh = 7 ² + 2(-10) (0) = 49 – 0 = 49

v _t = √49 = 7 m/s

Liwiro lomaliza panjira yopingasa

Liwiro loyambirira mbali yopingasa ndi 7 √ 3 m/s. Liwiro limakhala losasintha kotero kuti liwiro lomaliza likhale lofanana ndi liwiro loyambirira.

Liwiro lomaliza chinthucho chisanagwe pansi

2. Thupi limakwezedwa mmwamba pa ngodya ya 30 ^o ndi yopingasa kuchokera ku nyumba yokwera mamita 5. Liwiro lake loyamba ndi 10 m/s. Werengani liwiro lomaliza chinthucho chisanagunde pansi! Kuthamanga kwa mphamvu yokoka ndi 10 m/s ².

Zodziwika:

Ngodya ( θ ) = 30 ^o

Kutalika koyambirira (h _o ) = mamita 5

Liwiro loyambirira (v _o ) = 10 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Kufunidwa: Liwiro lomaliza

Yankho:

Gawo lolunjika la liwiro loyambirira:

v _ox = v _o cos θ = (10 m/s)(cos 30 ^o ) = (10 m/s) (0.5 √ 3 ) = 5 √ 3 m/s

Gawo loyima la liwiro loyambirira:

v _oy = v _o tchimo θ = (10 m/s) (tchimo 30 ^o ) = (10 m/s) (0.5) = 5 m/s

Liwiro lomaliza panjira yoyimirira

Zodziwika:

Liwiro loyambirira (v _o ) = 5 m/s (zabwino mmwamba)

Kuthamanga kwa mphamvu yokoka (g) = – 10 m/s ² (yoyipa pansi)

Kutalika (h) = -5 m ( kuchepa chifukwa nthaka ili pansi pa kutalika koyambirira)

Kufunidwa: Liwiro lomaliza (v _t )

Yankho:

v _t ² = v _o ² + 2 gh = 5 ² + 2(-10) (-5) = 25 + 100 = 125

v _t = √125 m/s

Liwiro lomaliza panjira yopingasa

Liwiro lomaliza panjira yopingasa ndi 5 √3 m/s.

Liwiro lomaliza

3. Mpira waung'ono umayesedwa mopingasa ndi liwiro loyambirira v _o = 8 m/s kuchokera ku nyumba ya mamita 12 kutalika. Werengani liwiro lomaliza mpira usanagwere pansi ! Kuthamanga kwa mphamvu yokoka ndi 10 m/s ²

Zodziwika:

Kutalika (h) = mamita 12

Liwiro loyambirira (v _o ) = 8 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Kufunidwa: Liwiro lomaliza (v _t )

Yankho:

Gawo lolunjika la liwiro loyambirira:

v _ng'ombe = v _o = 8 m/s

Gawo loyima la liwiro loyambirira:

v _oy = 0 m/s

Liwiro lomaliza panjira yoyimirira

kuwerengedwa pogwiritsa ntchito equation ya kuyenda kwaulere kwa kugwa.

Zodziwika:

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Kutalika (h) = 12 m

Kufunidwa: Liwiro lomaliza (v _t )

Yankho:

v _t ² = 2 gh = 2(10)(12) = 240

v _t = √240 m/s

Liwiro lomaliza panjira yopingasa

Liwiro loyamba mbali yopingasa ndi 8 m/s. Liwiro limakhala lokhazikika kotero kuti liwiro loyamba lifanane ndi liwiro lomaliza. Choncho liwiro lomaliza mbali yopingasa ndi 8 m/s.

Liwiro lomaliza

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1. Konzani liwiro loyambirira kukhala magawo opingasa ndi olunjika
2. Dziwani kusamuka kopingasa
3. Dziwani kutalika kwakukulu
4. Dziwani nthawi yomwe imatenga nthawi
5. Dziwani malo a chinthucho
6. Dziwani liwiro lomaliza

Werengani zambiri

Mavuto othetsedwa mu kayendedwe ka projectile - kudziwa malo a chinthu

1. Thupi limakwezedwa mmwamba pa ngodya ya 60 ^o kupita mopingasa ndi liwiro loyambirira la 12 m/s. Dziwani malo a chinthucho mutasuntha kwa sekondi imodzi! Kuthamanga kwa mphamvu yokoka ndi 10 m/s ².

Zodziwika:

Ngodya ( θ ) = 60 ^o

Liwiro loyambirira (v _o ) = 12 m/s

Nthawi yopuma (t) = sekondi imodzi

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Kufunidwa: Malo a chinthucho mutasuntha kwa sekondi imodzi

Yankho:

Gawo lolunjika la liwiro loyambirira:

v _ng'ombe = v _o cos θ = (12 m/s) (cos 60 ^o ) = (12 m/s) (0.5) = 6 m/s

Gawo loyima la liwiro loyambirira:

v _oy = v _o tchimo θ = (12 m/s)(tchimo 60 ^o ) = (12 m/s) (0.5 √ 3 ) = 6 √ 3 m/s

Malo a chinthucho molunjika:

Zodziwika:

Chigawo chopingasa cha liwiro (v _x ) = 6 m/s

Nthawi yopuma (t) = sekondi imodzi

Kufunidwa: malo opingasa (x)

Yankho:

Mamita 6/sekondi amatanthauza kuti mpira umayenda mamita 6 pa sekondi imodzi iliyonse. Mtunda wa mpira ukayenda kwa sekondi imodzi ndi mamita 6. Chifukwa chake malo a mpirawo mopingasa ndi mamita 6.

Malo a chinthucho panjira yoyimirira:

Sankhani njira yopita mmwamba ngati yabwino ndipo njira yopita pansi ngati yoipa.

Zodziwika:

Liwiro loyambirira (v _o ) = 6 √ 3 m/s (kukwera mmwamba)

Nthawi yopuma (t) = sekondi imodzi

Kuthamanga kwa mphamvu yokoka (g) = -10 m/s ² (yoyipa pansi)

Amafuna: kutalika atasuntha kwa sekondi imodzi

Yankho:

h = v_o t + 1/2 gt² = (6√3(1) + 1/2 (-10)(1)²) = 6√3 + (-5)(1) = 6√3 – 5 = 6(1.7) – 5 = 10.2 – 5 = mamita 5.2.

Malo a chinthucho mutasuntha kwa sekondi imodzi:

Kusuntha kopingasa (x) = mamita 6

Kusuntha koyima (y) = mamita 5.2

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2. Thupi limakwezedwa mmwamba pa ngodya ya 30 ^o kupita mopingasa kuchokera ku nyumba ya mamita 20 kutalika. Liwiro lake loyamba ndi 50 m/s. Werengani kusuntha koyima thupi likasuntha kwa sekondi imodzi! Kuthamanga kwa mphamvu yokoka ndi 10 m/s ².

Zodziwika:

Ngodya ( θ ) = 30 ^o

Kutalika koyambirira (h _o ) = mamita 20

Liwiro loyambirira (v _o ) = 50 m/s

Nthawi yopuma (t) = sekondi imodzi

Kuthamanga kwa mphamvu yokoka (g) = 1 0 m/s ²

Kufunidwa: Kutalika (h)

Yankho:

Gawo loyima la liwiro loyambirira:

v _oy = v _o tchimo θ = (50 m/s) (tchimo 30 ^o ) = (50 m/s) (0.5) = 25 m/s

Kutalika:

Sankhani njira yopita mmwamba ngati yabwino ndipo njira yopita pansi ngati yoipa.

Zodziwika:

Liwiro loyambirira (v _o ) = 25 m/s (zabwino mmwamba)

Nthawi yopuma (t) = sekondi imodzi

Kuthamanga kwa mphamvu yokoka (g) = -1 0 m/s ² (yoyipa pansi)

Kufunidwa: Kutalika (h)

Yankho:

h = vot ₊ 1/2 gt ^{​​​​2} = (25)(1) + 1/2 (-10)(1 ² ) = 25 + (-5)(1) = 25 - 5 = mamita 20.

Kutalika kwa thupi pambuyo posuntha kwa sekondi imodzi kumakhala mamita 20 pamwamba pa malo omwe thupilo lili kapena mamita 40 pamwamba pa nthaka.

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3. Mpira waung'ono umapimidwa mopingasa ndi liwiro loyambirira v _o = 10 m/s kuchokera ku nyumba ya mamita 10 kutalika. Werengani kusamuka kwa mpira mutasuntha kwa sekondi imodzi ! Kuthamanga kwa mphamvu yokoka ndi 10 m/s ²

Zodziwika:

Kutalika koyambirira (h) = mamita 10

Liwiro loyambirira (v _o ) = 10 m/s

Nthawi yopuma (t) = sekondi imodzi

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Akufuna: Malo a mpira atasuntha sekondi imodzi!

Yankho:

Kusamutsa kopingasa:

Zodziwika:

Chigawo chopingasa cha liwiro (v _x ) = 10 m/s

Nthawi yopuma (t) = sekondi imodzi

Kufunidwa: Malo a chinthucho

Yankho:

Mamita 10/sekondi amatanthauza kuti chinthucho chimayenda mpaka mamita 10 sekondi iliyonse. Kusuntha pambuyo posuntha kwa sekondi imodzi ndi mamita 10. Choncho kusuntha kopingasa ndi mamita 10.

Kusamutsa koyima:

Kuwerengedwa ngati kuyenda kwa free fall.

Zodziwika:

Nthawi yopuma (t) = sekondi imodzi

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Kufunidwa: Kutalika mutasuntha kwa sekondi imodzi (h)

Yankho:

h = 1/2 gt ^{​​​​2} = 1/2 (10)(1 ² ) = (5)(1) = mamita 5.

Pambuyo pa sekondi imodzi, chinthucho chimagwa mpaka mamita 5. Kutalika pamwamba pa nthaka = mamita 10 - mamita 5 = mamita 5.

Malo a chinthucho mutasuntha sekondi imodzi:

Malo a chinthucho mopingasa (x) = mamita 10

Malo a chinthucho pamalo oyima (y) = mamita 5

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1. Konzani liwiro loyambirira kukhala magawo opingasa ndi olunjika
2. Dziwani kusamuka kopingasa
3. Dziwani kutalika kwakukulu
4. Dziwani nthawi yomwe imatenga nthawi
5. Dziwani malo a chinthucho
6. Dziwani liwiro lomaliza

Werengani zambiri

Mavuto othetsedwa mu kayendedwe ka projectile - dziwani nthawi yomwe ikupita

1. Mpira wokankha umachoka pansi pa ngodya θ = 30 ^o kupita mopingasa ndi liwiro loyambirira la 10 m/s. Werengani nthawi yokwanira kuti mufike kutalika kwakukulu! Kuthamanga kwa mphamvu yokoka ndi 10 m/s ².

Zodziwika:

Ngodya (θ) = 3 0 ^o

Liwiro loyambirira (v _o ) = 10 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Kufunidwa: Nthawi yofikira kutalika kwakukulu

Yankho:

Gawo loyima la liwiro loyambirira:

v _oy = v _o tchimo θ = (10 m/s) (tchimo 30 ^o ) = (10 m/s) (0.5) = 5 m/s

Nthawi yoti mufike kutalika kwakukulu imatsimikiziridwa ndi equation yoyenda molunjika . Sankhani njira yopita mmwamba ngati yabwino ndi njira yotsika ngati yoipa.

Zodziwika:

Liwiro loyambirira (v _o ) = 5 m/s (zabwino mmwamba)

Kuthamanga kwa mphamvu yokoka (g) = – 10 m/s ² (yoyipa pansi)

Liwiro lomaliza pa kutalika kwakukulu (v _t ) = 0

Kufunidwa: nthawi yopuma (t)

Yankho:

v _t = vo _o + g t

0 = 5 + (-10)t

0 = 5 - 10 t

5 = 10 t

t = 5/10 = 0.5 s

[irp]

2. Thupi limakwezedwa mmwamba pa ngodya ya 30 ^o kupita mopingasa ndi liwiro loyambirira la 30 m/s. Werengani nthawi youluka! Kuthamanga kwa mphamvu yokoka ndi 10 m/s ².

Zodziwika:

Ngodya (θ) = 3 0 ^o

Liwiro loyambirira (v _o ) = 8 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Akufuna: Nthawi yopuma thupi lisanagwe pansi

Yankho:

Gawo loyima la liwiro loyambirira:

v _oy = v _o tchimo θ = (8 m/s) (tchimo 30 ^o ) = (8 m/s) (0.5) = 4 m/s

Choyamba timawerengera nthawi kuti tifike kutalika kwakukulu pogwiritsa ntchito equation ya kuyenda koyima.

Sankhani njira yopita mmwamba ngati yabwino ndipo njira yopita pansi ngati yoipa.

Zodziwika:

Liwiro loyambirira (v _o ) = 4 m/s (lokwera mmwamba)

Kuthamanga kwa mphamvu yokoka (g) = – 10 m/s ² (yoyipa pansi)

Liwiro lomaliza pa kutalika kwakukulu (v _t ) = 0

Kufunidwa: Nthawi yopuma (t)

Yankho:

v _t = vo _o + g t

0 = 4 + (-10)t

0 = 4 - 10 t

4 = 10 t

t = 4/10 = 0,4 s

Nthawi yoti mufike kutalika kwakukulu ndi masekondi 0.4.

Nthawi mumlengalenga ndi 2 x 0.4 s = 0.8 s.

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3. Thupi limakwezedwa mmwamba pa ngodya ya 30 ^o ndi kutalika kwa mamita 10 kuchokera ku nyumba. Liwiro lake loyamba ndi 40 m/s. Kodi thupi limatenga nthawi yayitali bwanji kuti lifike pansi? Kuthamanga kwa mphamvu yokoka ndi 10 m/s ².

Zodziwika:

Ngodya (θ) = 3 0 ^o

Kutalika koyambirira (h _o ) = mamita 10

Liwiro loyambirira (v _o ) = 40 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Kufunidwa: Nthawi mumlengalenga (t)

Yankho:

Gawo loyima la liwiro loyambirira:

v _oy = v _o tchimo θ = (40 m/s) (tchimo 30 ^o ) = (40 m/s) (0.5) = 20 m/s

Choyamba timawerengera nthawi kuti tifike kutalika kwakukulu pogwiritsa ntchito equation ya kuyenda koyima.

Sankhani njira yopita mmwamba ngati yabwino ndipo njira yopita pansi ngati yoipa.

Zodziwika:

Liwiro loyambirira (v _o ) = 20 m/s (lokwera mmwamba)

Kuthamanga kwa mphamvu yokoka (g) = – 10 m/s ² (yoyipa pansi)

Liwiro lomaliza pachimake (v _t ) = 0

Kufunidwa: Nthawi yopuma (t)

Yankho:

v _t = vo _o + g t

0 = 20 + (-10)t

0 = 20 - 10 t

20 = 10 t

t = 20/10 = masekondi awiri

Nthawi mumlengalenga = masekondi awiri x awiri = masekondi anayi.

Chinthucho chili pamtunda wa mamita 10 kuchokera pansi. Masekondi 4 ndi nthawi yoti mufike pamalo ofanana ndi malo oyamba. Mpirawo ukusunthirabe pansi.

Nthawi yofikira pansi imawerengedwa pogwiritsa ntchito equation ya kuyenda kwa free fall.

Zodziwika:

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Kutalika (h) = mamita 10

Kufunidwa: Nthawi yopuma (t)

Yankho:

h = 1/2 gt ^{​​​​2}

10 = 1/2 (10) t ²

10 = 5 t ²

t ² = 10/5 = 2

t = √2 = masekondi 1.4

Nthawi yopuma = masekondi 1.4.

Nthawi yonse = masekondi 4 + masekondi 1.4 = masekondi 5.4.

[irp]

4. Mpira waung'ono umapimidwa mopingasa ndi liwiro loyambirira v _o = 15 m/s kuchokera ku nyumba ya mamita 5 kutalika. Werengani nthawi mumlengalenga ! Kuthamanga kwa mphamvu yokoka ndi 10 m/s ²

Zodziwika:

Kutalika (h) = mamita 5

Liwiro loyambirira (v _o ) = 15 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Akufuna: Nthawi mlengalenga (t)

Yankho:

Nthawi yomwe ili mlengalenga imawerengedwa pogwiritsa ntchito equation ya kuyenda koyenda momasuka.

Zodziwika:

Kutalika (h) = mamita 5

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Kufunidwa: Nthawi yopuma (t)

Yankho:

h = 1/2 gt ^{​​​​2}

5 = 1/2 (10) t ²

5 = 5 t ²

t ² = 5/5 = 1

t = √1 = sekondi imodzi

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1. Konzani liwiro loyambirira kukhala magawo opingasa ndi olunjika
2. Dziwani kusamuka kopingasa
3. Dziwani kutalika kwakukulu
4. Dziwani nthawi yomwe imatenga nthawi
5. Dziwani malo a zinthu
6. Dziwani liwiro lomaliza

Werengani zambiri

Mavuto othetsedwa poyenda ndi zipolopolo - dziwani kutalika kwakukulu

1. Mpira wokankha umachoka pansi pa ngodya θ = 60 ^o ndipo wopingasa uli ndi liwiro loyambirira la 10 m/s. Werengani kutalika kwakukulu! Kuthamanga kwa mphamvu yokoka ndi 10 m/s ².

Zodziwika:

Ngodya (θ) = 60 ^o

Liwiro loyambirira (v _o ) = 10 m/s

Kufunidwa: Kutalika kwakukulu (h)

Yankho:

Gawo loyima la liwiro loyambirira:

sin 60 ^o = v _oy / vo _o

v _oy = v _o tchimo 60 ^o = (10)(tchimo 60 ^o ) = (10)(0.5 √ 3 ) = 5 √ 3 m/s

Sankhani njira yopita mmwamba ngati yabwino ndipo njira yopita pansi ngati yoipa.

Zodziwika:

Kuthamanga kwa mphamvu yokoka (g) = -10 m/s ² (yoyipa pansi)

Gawo loyima la liwiro loyambirira (v _oy ) = + 5 √ 3 m/s (zabwino mmwamba)

Liwiro lomaliza pa kutalika kwakukulu (v _ty ) = 0

Kufunidwa: Kutalika kwakukulu (h)

Yankho:

v _t ² = v _o ² + 2 gh

0 ² = ( 5 √ 3) ² + 2 (-10) h

0 = 2 5 ( 3) – maola 20

0 = maola 75 - 20

75 = maola 20

h = 75 / 20

h = mamita 3.75

Kutalika kwakukulu ndi mamita 3.75.

[irp]

2. Thupi limakwezedwa mmwamba pa ngodya ya 30 ^o ndipo mopingasa kuchokera ku nyumba yokwera mamita 20. Liwiro lake loyamba ndi 4 m/s. Werengani kutalika kwakukulu! Kuthamanga kwa mphamvu yokoka ndi 10 m/s ².

Zodziwika:

Ngodya (θ) = 30 ^o

Kutalika koyambirira (h) = mamita 20

Liwiro loyambirira (v _o ) = 4 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Kufunidwa: Kutalika kwakukulu (h)

Yankho:

Gawo loyima la liwiro loyambirira:

sin 30 ^o = v _oy / vo _o

v _oy = v _o tchimo 30 ^o = (4) (tchimo 30 ^o ) = (4) (0.5) = 2 m/s

Sankhani njira yopita mmwamba ngati yabwino ndipo njira yopita pansi ngati yoipa.

Zodziwika:

Kuthamanga kwa mphamvu yokoka (g) = -10 m/s ² (yoyipa pansi)

Gawo loyima la liwiro loyambirira (v _oy ) = +2 m/s (zabwino mmwamba)

Liwiro lomaliza pa kutalika kwakukulu (v _ty ) = 0

Kufunidwa: Kutalika kwakukulu

Yankho:

Kutalika kwakukulu:

v _t ² = v _o ² + 2 gh

0 ² = 2 ² + 2 (-10) h

0 = maola 4 - 20

4 = maola 20

h = 4 / 20

h = mamita 0.2

Kutalika kwakukulu ndi mamita 0.2 + mamita 20 = mamita 20.2.

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1. Konzani liwiro loyambirira kukhala magawo opingasa ndi olunjika
2. Dziwani kusamuka kopingasa
3. Dziwani kutalika kwakukulu
4. Dziwani nthawi yomwe imatenga nthawi
5. Dziwani malo a zinthu
6. Dziwani liwiro lomaliza

Werengani zambiri

Mavuto othetsedwa mu kayendedwe ka projectile - dziwani kusamuka kopingasa

1. Mpira wokankha umachoka pansi pa ngodya θ = 60 ^o ndipo wopingasa uli ndi liwiro loyamba la 16 m/s. Kodi zidzatenga nthawi yayitali bwanji mpira usanagwe pansi?

Zodziwika:

Ngodya ( θ ) = 60 ^o

Liwiro loyambirira (v _o ) = 16 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Kufunidwa: Kusamutsa kopingasa (x)

Yankho:

Gawo lolunjika la liwiro loyambirira:

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

Gawo loyima la liwiro loyambirira:

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

Kuyenda kwa projectile kungamveke bwino pofufuza zigawo zopingasa ndi zoyima za kuyendako padera. Kuyenda kwa x kumachitika pa liwiro losasintha ndipo kuyenda kwa y kumachitika pa liwiro losasintha la mphamvu yokoka.

Nthawi mlengalenga

Nthawi yomwe imakhala mlengalenga imatsimikiziridwa ndi kayendedwe ka y. Choyamba timapeza nthawi pogwiritsa ntchito kayendedwe ka y kenako timagwiritsa ntchito mtengo wa nthawi iyi mu ma equation a x ( equation ya liwiro lokhazikika ).

Sankhani njira yopita mmwamba ngati yabwino ndipo njira yopita pansi ngati yoipa.

Zodziwika:

Liwiro loyambirira (v _o ) = 8 √ 3 m/s (v _o mmwamba)

Kuthamanga kwa mphamvu yokoka (g) = -10 m/s ² (g pansi)

Kutalika (h) = 0 (mpira wabwerera pamalo omwewo)

Akufuna: Nthawi Mumlengalenga

Yankho:

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 = masekondi 2.8

Kusamutsa kopingasa

Zodziwika:

Liwiro (v) = 8 m/s

Nthawi yopuma (t) = masekondi 2.8

Kufunidwa: Kusamutsidwa

Yankho:

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

Kusuntha kopingasa ndi mamita 22.4.

[irp]

2. Thupi limakwezedwa mmwamba pa ngodya ya 60 ^o ndipo mopingasa kuchokera ku nyumba yokwera mamita 50. Liwiro lake loyamba ndi 30 m/s. Werengani kusuntha kopingasa! Kuthamanga kwa mphamvu yokoka ndi 10 m/s ².

Zodziwika:

Ngodya ( θ ) = 60 ^o

Kutalika (h) = 15 m

Liwiro loyambirira (v _o ) = 30 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Akufuna: x

Yankho:

Gawo lolunjika la liwiro loyambirira ::

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

Gawo loyima la liwiro loyambirira:

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

Nthawi mlengalenga

Choyamba timapeza nthawi pogwiritsa ntchito kayendedwe ka y kenako timagwiritsa ntchito mtengo wa nthawi iyi mu ma equation a x (equation ya liwiro lokhazikika). Sankhani mmwamba ngati zabwino komanso pansi ngati zoipa.

Zodziwika:

Liwiro loyambirira (v _o ) = 15 √ 3 m/s (kukwera mmwamba)

Kuthamanga kwa mphamvu yokoka (g) = -10 m/s ² (yoyipa pansi)

Kutalika (h) = -50 (Pansi mamita 50 pansi pa malo oyamba)

Ankafuna: t

Yankho:

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

Werengerani nthawi pogwiritsa ntchito fomula iyi:

a = 5, b = – 15 √ 3, c = – 50

Nthawi yomwe ili mlengalenga ndi masekondi 6.7.

Kusamutsa kopingasa:

Zodziwika:

Liwiro (v) = 15 m/s

Nthawi yopuma (t) = masekondi 6.7

Kufunidwa: kusamutsidwa

Yankho:

s = vt = (15 m/s)(6.7 s) = mamita 100.5

Kusuntha kopingasa ndi mamita 100.5.

[irp]

3. Mpira waung'ono umapimidwa mopingasa ndi liwiro loyambirira v _o = 10 m/s kuchokera ku nyumba ya mamita 10 kutalika. Werengani kusuntha kopingasa ! Kuthamanga kwa mphamvu yokoka ndi 10 m/s ²

Zodziwika:

Kutalika (h) = 10 m

Liwiro loyambirira (v _o ) = 10 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Akufuna: x

Yankho:

Gawo lolunjika la liwiro loyambirira = liwiro loyambirira = 10 m/s.

Nthawi mlengalenga

Nthawi yomwe ili mumlengalenga imawerengedwa pogwiritsa ntchito equation ya kuyenda kwaulere kwa kugwa.

Zodziwika:

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

Kutalika (h) = mamita 10

Ankafuna: t

Yankho:

h = 1/2 gt ^{​​​​2}

10 = 1/2 (10) t ²

10 = 5 t ²

t ² = 10 / 5 = 2

t = √2 = masekondi 1.4

Kusamutsa kopingasa

Kusuntha kopingasa kumawerengedwa pogwiritsa ntchito equation ya kuyenda pa liwiro losasintha.

Zodziwika:

Liwiro (v) = 10 m/s

Nthawi yopuma (t) = masekondi 1.4

Akufuna: x

Yankho:

s = vt = (10 m/s)(1.4 s) = mamita 14

Kusuntha kopingasa ndi mamita 14.

[irp]

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1. Konzani liwiro loyambirira kukhala magawo opingasa ndi olunjika
2. Dziwani kusamuka kopingasa
3. Dziwani kutalika kwakukulu
4. Dziwani nthawi yomwe imatenga nthawi
5. Dziwani malo a zinthu
6. Dziwani liwiro lomaliza

Werengani zambiri

Mavuto othetsedwa pakuyenda kwa projectile - adathetsa liwiro loyambirira kukhala magawo opingasa ndi olunjika

1. Mpira wokankha umachoka pansi pa ngodya θ = 60^o ndi liwiro la 10 m/s. Werengani zigawo zoyambira za liwiro!
Zodziwika:
Ngodya (θ) = 60^o
Liwiro loyambirira (v)_o) = 10 m/s
Akufuna: v_ox ndi v_oy
Yankho:
Konzani liwiro loyambirira kukhala gawo la x (lopingasa) ndi gawo la y (lopingasa).
tchimo θ = v_oy /v_o —–> v_oy =v_o tchimo θ
cos θ = v_ox /v_o —–> v_ox =v_o cos θ

gawo la x (lopingasa):
v_ox =v_o cos θ = (10 m/s)(cos 60^o) = (10 m/s)(0.5) = 5 m/s

gawo la y (loyima):
v_oy =v_o uchimo θ = (10 m/s)(uchimo 60^o) = (10 m/s)(0.5√3) = 5√3 m/s

[irp]

2. Chinthu chimachoka pansi pa ngodya θ = 30^o ndi gawo la y la liwiro la 10 m/s. Werengani liwiro loyambirira!
Zodziwika:
Ngodya (θ) = 30^o
gawo la y (v)_oy) = 10 m/s
Akufuna: Liwiro loyambirira (v)_o)
Yankho:
v_oy =v_o tchimo θ
10 = (v_o)chimo 30^o)
10 = (v_o) (0.5)
v_o = 10/0.5
v_o = 20 m/s

[irp]

3. Chigawo chopingasa cha liwiro loyambira ndi 30 m/s ndipo chigawo chopingasa cha liwiro loyambira ndi 40 m/s. Werengani liwiro loyambira.
Zodziwika:
Gawo lolunjika la liwiro loyambirira (v)_ox) = 30 m/s
Gawo loyima la liwiro loyambirira (v)_oy) = 40 m/s
Akufuna: Liwiro loyambirira (v)_o)
Yankho:
v_o² =v_ox² +v_oy² = 30² + 40² 900 + 1600 = 2500
v_o = √2500
v_o = 50 m/s

[irp]

4. Mpira wawung'ono umayendetsedwa mopingasa ndi liwiro loyambirira v_o = 6m/s. Werengani gawo la x ndi gawo la y la liwiro loyambirira.
Zodziwika:
Liwiro loyambirira (v)_o) = 6 m/s
Akufuna: vox ndi v_oy
Yankho:
Mpira umayenda mopingasa kotero kuti gawo lopingasa la liwiro (v)_ox) = liwiro loyambirira (v_o) = 6 m/s. Chigawo choyima cha liwiro (v)_oy) = 0.

[irp]

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[wpdm_package id='536′]

1. Konzani liwiro loyambirira kukhala magawo opingasa ndi olunjika
2. Dziwani kusamuka kopingasa
3. Dziwani kutalika kwakukulu
4. Dziwani nthawi yomwe imatenga nthawi
5. Dziwani malo a zinthu
6. Dziwani liwiro lomaliza

Werengani zambiri