Mavuto Othetsedwa mu Fiziki Yoyambira

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

Zodziwika:

Ngodya (θ= = 30^o

Liwiro loyambirira (v_o) = 14 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m / s²

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 uchimo θ = (14 m/s)(uchimo 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 / s² (zoyipa pansi)

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

Akufuna: Liwiro lomaliza (v)_t)

Yankho:

v_t² =v_o² + 2 gh = 7² + 2(-10)(0) = 49 – 0 = 49

v_t = √49 = 7 m/s

Liwiro lomaliza panjira yopingasa

Liwiro loyamba panjira yopingasa ndi 7√3 m/s. Liwiro ndi lokhazikika 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 yotalika mamita 5. Liwiro lake loyamba ndi 10 m/s. Werengani liwiro lomaliza chinthucho chisanagwe pansi! Kuthamanga kwa mphamvu yokoka ndi 10 m/s².

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/s²

Akufuna: 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 uchimo θ = (10 m/s)(uchimo 30^o) = (10 m/s)(0.5) = 5 m/s

Liwiro lomaliza panjira yoyimirira

Zodziwika:

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

mofulumira mphamvu yokoka (g) = –10 m / s² (zoyipa pansi)

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

Akufuna: Liwiro lomaliza (v)_t)

Yankho:

v_t² =v_o² + 2 gh = 5² + 2(-10)(-5) = 25 + 100 = 125

v_t = √125 m/s

Liwiro lomaliza panjira yopingasa

Liwiro lomaliza panjira yopingasa ndi 5.3 Ms.

Liwiro lomaliza

3. Mpira wawung'ono woponyedwa mopingasa ndi liwiro loyambirira v_o = 8 m/s kuchokera ku nyumba yokwera mamita 12. Werengani liwiro lomaliza mpira usanagwe pansiKuthamanga kwa mphamvu yokoka ndi 10 m/s²

Zodziwika:

Kutalika (h) = mamita 12

Liwiro loyambirira (v)_o) = 8 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s²

Akufuna: Liwiro lomaliza (v)_t)

Yankho:

Gawo lolunjika la liwiro loyambirira:

v_ox =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 / s²

Kutalika (h) = 12 m

Akufuna: Liwiro lomaliza (v)_t)

Yankho:

v_t² = 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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[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 chinthucho
6. Dziwani liwiro lomaliza

Werengani zambiri

Mavuto othetsedwa pakuyenda kwa projectile - kudziwa malo a chinthu

1. Thupi limakwezedwa mmwamba pa ngodya ya 60^o ku yopingasa yokhala ndi liwiro loyambirira la 12 m/s. Dziwani malo a chinthucho mutasuntha kwa sekondi imodzi! Kuthamanga kwa mphamvu yokoka ndi 10 m/s².

Zodziwika:

Ngodya (θ) = 60^o

Poyamba kuthamanga (v_o) = 12 m/s

Nthawi yopuma (t) = sekondi imodzi

Kuthamanga kwa mphamvu yokoka (g) = 10 m / s²

Akufuna: Malo a chinthucho mutasuntha kwa sekondi imodzi

Yankho:

Gawo lolunjika la liwiro loyambirira:

v_ox =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 uchimo θ = (12 m/s)(uchimo 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

Akufuna: 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 (zabwino mmwamba)

Nthawi yopuma (t) = sekondi imodzi

Kuthamanga kwa mphamvu yokoka (g) = -10 m/s² (zoyipa pansi)

Akufuna: kutalika mutasuntha 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

2. Thupi limakwezedwa mmwamba pa ngodya ya 30^o ku chiwongolero chopingasa kuchokera ku nyumba yotalika mamita 20. Liwiro lake loyamba ndi 50 m/s. Werengani kusuntha koyima thupi likasuntha kwa sekondi imodzi! Kuthamanga kwa mphamvu yokoka ndi 10 m/s².

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) = 10 m / s²

Akufuna: Kutalika (h)

Yankho:

Gawo loyima la liwiro loyambirira:

v_oy =v_o uchimo θ = (50 m/s)(uchimo 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) = -10 m / s² (zoyipa pansi)

Akufuna: Kutalika (h)

Yankho:

h = v_o t + 1/2 gt² = (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 kuchokera pomwe thupi lili zanenedwa kapena mamita 40 pamwamba pa nthaka.

3. Mpira wawung'ono woponyedwa mopingasa ndi liwiro loyambirira v_o = 10 m/s kuchokera ku nyumba yokwera mamita 10. Werengani kusuntha kwa mpira mutatha kusuntha kwa sekondi imodziKuthamanga kwa mphamvu yokoka ndi 10 m/s²

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/s²

SE basi: Malo a mpira mutasuntha sekondi imodzi!

Yankho:

Kusamutsa kopingasa:

Zodziwika:

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

Nthawi yopuma (t) = sekondi imodzi

SE basi: Malo a chinthucho

Yankho:

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

Kusamutsa koyima:

Zowerengedwa ngati kuyenda kwaulere kwa kugwa.

Zodziwika:

Nthawi yopuma (t) = sekondi imodzi

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s²

Akufuna: Kutalika mutasuntha kwa sekondi imodzi (h)

Yankho:

h = 1/2 gt² = 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 pa njira yopingasa (x) = mamita 10

Malo a chinthucho pamalo oyima (y) = mamita 5

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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 chinthucho
6. Dziwani liwiro lomaliza

Werengani zambiri

Mavuto othetsedwa pakuyenda kwa projectile - kudziwa nthawi yopuma

1. Mpira wokankha umachoka pansi pa ngodya θ = 30^o kulowera mopingasa ndi liwiro loyambirira la 10 m/s. Werengani nthawi yokwanira kuti mufike kutalika kwakukulu! Kuthamanga kwa mphamvu yokoka ndi 10 m/s².

Zodziwika:

Ngodya (θ) = 30^o

Liwiro loyambirira (v)_o) = 10 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s²

Akufuna: Nthawi yofikira pa kutalika kwakukulu

Yankho:

Gawo loyima la liwiro loyambirira:

v_oy =v_o uchimo θ = (10 m/s)(uchimo 30^o) = (10 m/s)(0.5) = 5 m / s

Nthawi yofikira kutalika kwakukulu imatsimikiziridwa ndi kuyenda koyima Sankhani njira yopita mmwamba ngati yabwino ndi njira yotsikira pansi ngati yoipa.

Zodziwika:

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

Kuthamanga kwa mphamvu yokoka (g) = –10 m / s² (zoyipa pansi)

Liwiro lomaliza pa kutalika kwakukulu (v)_t= = 0

Akufuna: nthawi yopuma (t)

Yankho:

v_t =v_o + gt

0 = 5 + (-10)t

0 = 5 - 10 t

5 = 10 t

t = 5/10 = 0.5 s

2. Thupi limakwezedwa mmwamba pa ngodya ya 30^o ku yopingasa yokhala ndi liwiro loyambirira la 30 m/s. Werengani nthawi youluka! Kuthamanga kwa mphamvu yokoka ndi 10 m/s².

Zodziwika:

Ngodya (θ) = 30^o

Liwiro loyambirira (v)_o) = 8 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m / s²

Akufuna: Nthawi yopuma thupi lisanagwe pansi

Yankho:

Gawo loyima la liwiro loyambirira:

v_oy =v_o uchimo θ = (8 m/s)(uchimo 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 (zabwino mmwamba)

Kuthamanga kwa mphamvu yokoka (g) = –10 m / s² (zoyipa pansi)

Liwiro lomaliza pa kutalika kwakukulu (v)_t= = 0

Akufuna: Nthawi yopuma (t)

Yankho:

v_t =v_o + gt

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.

3. Thupi limakwezedwa mmwamba pa ngodya ya 30^o ndi yopingasa kuchokera ku nyumba yotalika mamita 10. Liwiro lake loyamba ndi 40 m/s. Kodi thupi limatenga nthawi yayitali bwanji kuti lifike pansi? Kuthamanga kwa mphamvu yokoka ndi 10 m/s².

Zodziwika:

Ngodya (θ) = 30^o

Kutalika koyambirira (h)_o) = mamita 10

Liwiro loyambirira (v)_o) = 40 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m / s²

Akufuna: Nthawi mumlengalenga (t)

Yankho:

Gawo loyima la liwiro loyambirira:

v_oy =v_o uchimo θ = (40 m/s)(uchimo 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 (zabwino mmwamba)

Kuthamanga kwa mphamvu yokoka (g) = –10 m / s² (zoyipa pansi)

Liwiro lomaliza pachimake (v)_t= = 0

Akufuna: Nthawi yopuma (t)

Yankho:

v_t =v_o + gt

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 kwaulere kwa kugwa. 

Zodziwika:

Kuthamanga kwa mphamvu yokoka (g) = 10 m / s²

Kutalika (h) = mamita 10

Akufuna: Nthawi yopuma (t)

Yankho:

h = 1/2 gt²

10 = 1/2 (10) t²

10 = 5 t²

t² = 10/5 = 2

t = √2 = masekondi 1.4

Nthawi yopuma = masekondi 1.4.

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

4. Mpira wawung'ono woponyedwa mopingasa ndi liwiro loyambirira v_o = 15 m/s kuchokera ku nyumba ya mamita 5 kutalika. Werengani nthawi mumlengalengaKuthamanga kwa mphamvu yokoka ndi 10 m/s²

Zodziwika:

Kutalika (h) = mamita 5

Liwiro loyambirira (v)_o) = 15 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s²

SE basi: Nthawi mumlengalenga (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/s²

Akufuna: Nthawi yopuma (t)

Yankho:

h = 1/2 gt²

5 = 1/2 (10) t²

5 = 5 t²

t² = 5/5 = 1

t = √1 = sekondi imodzi

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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

Mavuto othetsedwa pakuyenda kwa projectile - dziwani kutalika kwakukulu

1. Mpira wokankha umachoka pansi pa ngodya θ = 60^o ndi yopingasa ili ndi liwiro loyambirira la 10 m/s. Werengani kutalika kwakukulu! Kuthamanga kwa mphamvu yokoka ndi 10 m/s².

Zodziwika:

Ngodya (θ) = 60^o

Liwiro loyambirira (v)_o) = 10 m/s

Akufuna: Kutalika kwakukulu (h)

Yankho:

Gawo loyima la liwiro loyambirira:

tchimo 60^o =v_oy /v_o

v_oy =v_o tchimo 60^o = (10)(chimo 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/s² (zoyipa pansi)

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

Liwiro lomaliza pa kutalika kwakukulu (v)_ty= = 0

Akufuna: Kutalika kwakukulu (h)

Yankho:

v_t² =v_o² + 2 gh

0² = (5√3)² + 2 (-10) maola

0 = 25(3) – maola 20

0 = 75 – maola 20

75 = 20 h

h = 75 / 20

h = mamita 3.75

Kutalika kwakukulu ndi mamita 3.75.

2. Thupi limakwezedwa mmwamba pa ngodya ya 30^o ndi yopingasa kuchokera ku nyumba yokwera mamita 20. Liwiro lake loyamba ndi 4 m/s. Werengani kutalika kwakukulu! Kuthamanga kwa mphamvu yokoka ndi 10 m/s².

Zodziwika:

Ngodya (θ) = 30^o

Kutalika koyambirira (h) = mamita 20

Liwiro loyambirira (v_o) = 4 m/s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s²

Akufuna: Kutalika kwakukulu (h)

Yankho:

Gawo loyima la liwiro loyambirira:

tchimo 30^o =v_oy /v_o

v_oy =v_o tchimo 30^o = (4)(chimo 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/s² (zoyipa pansi)

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

Liwiro lomaliza pa kutalika kwakukulu (v)_ty= = 0

Akufuna: Kutalika kwakukulu

Yankho:

Kutalika kwakukulu:

v_t² =v_o² + 2 gh

0² = 2² + 2 (-10) maola

0 = 4 – maola 20

4 = 20 h

h = 4 / 20

h = mamita 0.2

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

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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

Mavuto othetsedwa pakuyenda kwa projectile - dziwani kusamuka kopingasa

1. Mpira wokankha umachoka pansi pa ngodya θ = 60^o ndi yopingasa ili 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/s²

Akufuna: Kusamutsa kopingasa (x)

Yankho:

Gawo lolunjika la liwiro loyambirira:

v_ox =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 uchimo θ = (16 m/s)(uchimo 60^o) = (16 m/s)(0.5√3= = 8√3 m / s

projectile-kuyenda Kutha kumveka bwino pofufuza zigawo zopingasa ndi zoyima za kayendedwe 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 (liwiro losasintha equation).

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/s² (g pansi)

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

Akufuna: Nthawi mumlengalenga

Yankho:

h = v_o t + 1/2 gt²

0 = (8√3) t + 1/2 (-10) t²

0 = 8√3 t – 5 t²

8√3 t = 5 t²

8 (1.7) = 5 t

14 = 5 t

t = 14 / 5 = masekondi 2.8

Kusamutsa kopingasa

Zodziwika:

mathamangidwe (v) = 8 m/s

Nthawi yopuma (t) = masekondi 2.8

Akufuna: Kusuntha

Yankho:

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

Kusuntha kopingasa ndi mamita 22.4.

2. Thupi limakwezedwa mmwamba pa ngodya ya 60^o ndi yopingasa kuchokera ku nyumba yotalika mamita 50. Liwiro lake loyamba ndi 30 m/s. Werengani kusuntha kopingasa! Kuthamanga kwa mphamvu yokoka ndi 10 m/s².

Zodziwika:

Ngodya (θ) = 60^o

Kutalika (h) = 15 m

Liwiro loyambirira (v)_o= = 30 m / s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s²

Akufuna: x

Yankho:

Gawo lolunjika la liwiro loyambirira ::

v_ox =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 uchimo θ = (30 m/s)(uchimo 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 (zabwino mmwamba)

Kuthamanga kwa mphamvu yokoka (g) = -10 m/s² (zoyipa pansi)

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

Akufuna: t

Yankho:

h = v_o t + 1/2 gt²

-50 = (15√3) t + 1/2 (-10) t²

-50 = 15√3 t – 5 t²

5 t² - 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

Akufuna: kusamuka

Yankho:

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

Kusuntha kopingasa ndi mamita 100.5.

3. Mpira wawung'ono woponyedwa mopingasa ndi liwiro loyambirira v_o = 10 m/s kuchokera ku nyumba ya mamita 10 kutalika. Werengani kusuntha kopingasaKuthamanga kwa mphamvu yokoka ndi 10 m/s²

Zodziwika:

Kutalika (h) = 10 m

Liwiro loyambirira (v)_o= = 10 m / s

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s²

Akufuna: x

Yankho:

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

Nthawi mlengalenga

Nthawi yomwe ili mumlengalenga imawerengedwa pogwiritsa ntchito kuyenda kwaulere kwa kugwa mayikidwe

Zodziwika:

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s²

Kutalika (h) = mamita 10

Akufuna: t

Yankho:

h = 1/2 gt²

10 = 1/2 (10) t²

10 = 5 t²

t² = 10/5 = 2

t = √2 = masekondi 1.4

Kusamutsa kopingasa

Kusamuka 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.

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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 - sinthani 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

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

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

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.

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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