Chitsanzo cha funso loti mudziwe nthawi yomwe kayendedwe ka parabolic kamachitika

Zitsanzo 4 za mafunso oti mudziwe nthawi yoyenda mozungulira

1. Mpira umakankhidwa mmwamba pa ngodya 30^o motsutsana ndi pamwamba pa bwalo ndi liwiro loyambirira la 10 m/s. Dziwani nthawi yomwe mpirawo ufike kutalika kwake kwakukulu! Kuthamanga kwa mphamvu yokoka = 10 m/s²
Zokambirana
Amadziwika kuti:
Ngodya (θ) = 30^o
Kecepatan chiyambi (v)_o) = 10 m/s
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa kuti: Nthawi yoti mpira ufike kutalika kwake kwakukulu
Yankho:
Liwiro loyamba la mpira mbali yowongoka:
v_oy =v_o uchimo θ = (10 m/s)(uchimo 30^o) = (10 m/s)(0,5) = 5 m/s

Nthawi yomwe mpira ufike kutalika kwake kwakukulu imawerengedwa pogwiritsa ntchito fomulayi kuyenda koyima mmwamba.
Pothetsa mavuto okhudzana ndi kuyenda molunjika mmwamba, kuchuluka kwa vekitala komwe kumatsogozedwa mmwamba kumapatsidwa chizindikiro chabwino, kuchuluka kwa vekitala njira yopita pansi imapatsidwa chizindikiro chotsutsa.
Amadziwika kuti:
Liwiro loyambirira (v)_o) = 5 m/s (zabwino chifukwa chiwongolero cha liwiro loyambirira chili mmwamba)
Kuthamanga chifukwa cha mphamvu yokoka (g) = -10 m/s² (zoipa chifukwa njira yokoka imayendera pansi)
Liwiro lomaliza (v)_t) = 0 (pa kutalika kwakukulu, chinthucho chimakhalabe kwakanthawi chisanasinthe njira)
Anafunsa kuti: Nthawi yopuma (t)
Yankho:
Zikudziwika kuti v_o, g ndi v_t, adafunsa t kotero fomula v imagwiritsidwa ntchito_t =v_o + gt
v_t =v_o + gt
0 = 5 + (-10)t
0 = 5 - 10 t
5 = 10 t
t = 5/10 = masekondi awiri
Nthawi yoti mpira ufike kutalika kwake kwakukulu ndi masekondi awiri.

2. Mpirawo umaponyedwa mmwamba pa ngodya ya 30^o mopingasa ndi liwiro loyamba la 8 m/s. Kodi zimatenga nthawi yayitali bwanji kuti mpira ufikekuyenda kwa parabolicKuthamanga chifukwa cha mphamvu yokoka = 10 m/s²
Zokambirana
Amadziwika kuti:
Ngodya (θ) = 30^o
Liwiro loyambirira (v)_o) = 8 m/s
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa kuti: Nthawi yoti mpira usunthire mu parabola
Yankho:
Liwiro loyamba la mpira mbali yowongoka:
v_oy =v_o uchimo θ = (8 m/s)(uchimo 30^o) = (8 m/s)(0,5) = 4 m/s

Choyamba, werengani nthawi yomwe chinthucho chifike kutalika kwake kwakukulu pogwiritsa ntchito njira yoyendetsera molunjika mmwamba.
Pothetsa mavuto oyenda molunjika mmwamba, kuchuluka kwa vekitala komwe kumatsogozedwa mmwamba kumapatsidwa chizindikiro chabwino, kuchuluka kwa vekitala komwe kumatsogozedwa pansi kumapatsidwa chizindikiro choipa.
Amadziwika kuti:
Liwiro loyambirira (v)_o) = 4 m/s (zabwino chifukwa chiwongolero cha liwiro loyambirira chili mmwamba)
Kuthamanga chifukwa cha mphamvu yokoka (g) = -10 m/s² (zoipa chifukwa njira yokoka imayendera pansi)
Liwiro lomaliza (v)_t) = 0 (pa kutalika kwakukulu, chinthucho chimakhalabe kwakanthawi chisanasinthe njira)
Anafunsa kuti: Nthawi yopuma (t)
Yankho:
Zikudziwika kuti v_o, g ndi v_t, anafunsa t kotero fomula imagwiritsidwa ntchito v_t =v_o + gt
v_t =v_o + gt
0 = 4 + (-10)t
0 = 4 - 10 t
4 = 10 t
t = 4/10 = masekondi awiri
Nthawi yoti mpira ufike kutalika kwake kwakukulu ndi masekondi awiri.
Njira ya mpira ndi yofanana, kotero nthawi yomwe mpira uyenera kupita mmwamba ndi yofanana ndi nthawi yomwe mpira uyenera kupita pansi. Choncho nthawi yonseyi ndi masekondi awiri x 0,4 = masekondi 0,8.

3. Chipolopolocho chimawomberedwa mmwamba pa ngodya ya 30°^o Kuthamanga mopingasa kuchokera pamalo okwana mamita 10 kuchokera pansi. Liwiro loyamba la chipolopolo ndi 40 m/s. Kodi zimatenga nthawi yayitali bwanji kuti chipolopolocho chifike pansi? Kuthamanga chifukwa cha mphamvu yokoka ndi 10 m/s²
Zokambirana
Amadziwika kuti:
Ngodya (θ) = 30^o
Kutalika koyambirira (h)_o) = mamita 10
Liwiro loyambirira (v)_o) = 40 m/s
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa kuti: Nthawi yomwe chipolopolo chili mlengalenga
Yankho:
Liwiro loyamba la mpira mbali yowongoka:
v_oy =v_o uchimo θ = (40 m/s)(uchimo 30^o) = (40 m/s)(0,5) = 20 m/s

Choyamba, werengani nthawi yomwe chipolopolocho chifike kutalika kwake kwakukulu pogwiritsa ntchito njira yoyendetsera molunjika mmwamba.
Pothetsa mavuto oyenda molunjika mmwamba, kuchuluka kwa vekitala komwe kumatsogozedwa mmwamba kumapatsidwa chizindikiro chabwino, kuchuluka kwa vekitala komwe kumatsogozedwa pansi kumapatsidwa chizindikiro choipa.
Amadziwika kuti:
Liwiro loyambirira (v)_o) = 20 m/s (zabwino chifukwa chiwongolero cha liwiro loyambirira chili mmwamba)
Kuthamanga chifukwa cha mphamvu yokoka (g) = -10 m/s² (zoipa chifukwa njira yokoka imayendera pansi)
Liwiro lomaliza (v)_t) = 0 (pa kutalika kwakukulu, chinthucho chimakhalabe kwakanthawi chisanasinthe njira)
Anafunsa kuti: Nthawi yopuma (t)
Yankho:
Zikudziwika kuti v_o, g ndi v_t, anafunsa t kotero fomula imagwiritsidwa ntchito v_t =v_o + gt
v_t =v_o + gt
0 = 20 + (-10)t
0 = 20 - 10 t
20 = 10 t
t = 20/10 = masekondi awiri
Nthawi yoti mpira ufike kutalika kwake kwakukulu ndi masekondi awiri.
Njira ya mpira ndi yofanana kotero nthawi yomwe mpira uli mlengalenga ndi masekondi awiri ndi awiri = masekondi anayi.

Chipolopolo chimawomberedwa kuchokera pamalo omwe ali mamita 10 kuchokera pansi. Zimatenga masekondi anayi kuti mpira ufike pomwe umayambira. Mpirawo umapitirira kuyenda pansi.

Nthawi yoti mpira usunthire pansi kuchokera kutalika kwa mamita 10 imawerengedwa kuti idziwe nthawi yoti ugwere momasuka.
Amadziwika kuti:
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Kutalika (h) = mamita 10
Anafunsa kuti: Nthawi yopuma (t)
Yankho:
Kuperekedwa g, h ndi kufunsidwa t kotero kuti njira yoyendetsera yoyenda yaulere yogwiritsidwa ntchito ndi h = 1/2 gt²
h = 1/2 gt²
10 = 1/2 (10) t²
10 = 5 t²
t² = 10/5 = 2
t = √2 = masekondi 1,4
Nthawi yomwe chipolopolo chigwe kuchokera kutalika kwa mamita 10 ndi sekondi imodzi.

Nthawi yonse yomwe chipolopolo chili mlengalenga ndi masekondi 4 + masekondi 1,4 = masekondi 5,4.

4. Marble imaponyedwa mopingasa kumanja kuchokera kutalika kwa mamita 5 ndi liwiro loyambirira la 15 m/s. Dziwani nthawi yomwe marble ili mlengalenga! Kuthamanga chifukwa cha mphamvu yokoka = 10 m/s²
Zokambirana
Amadziwika kuti:
Kutalika (h) = mamita 5
Liwiro loyambirira (v)_o) = 15 m/s
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa kuti: Nthawi yomwe miyala ya marble ili mlengalenga
Yankho:
Njira ya marble ndi monga momwe zasonyezedwera pachithunzichi. Nthawi yomwe marble ili mlengalenga imawerengedwa pogwiritsa ntchito njira iyi kuyenda kwaulere kwa kugwa.
Amadziwika kuti:
Kutalika (h) = mamita 5
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²

Anafunsa kuti: Nthawi yopuma (t)
Yankho:
Kuperekedwa g, h ndi kufunsidwa t kotero kuti njira yoyendetsera yoyenda yaulere yogwiritsidwa ntchito ndi h = 1/2 gt²
h = 1/2 gt²
5 = 1/2 (10) t²
5 = 5 t²
t² = 5/5 = 1
t = √1 = masekondi 1
Nthawi yomwe chipolopolo chigwe kuchokera kutalika kwa mamita 5 ndi sekondi imodzi.

[Chingerezi: Kuthetsa mavuto oyenda ndi zombo - kudziwa nthawi yopuma ]