Chitsanzo cha funso loti mudziwe mtunda wautali kwambiri wa kayendedwe ka parabolic

Zitsanzo zitatu za mafunso oti mudziwe mtunda wautali kwambiri wa kayendedwe ka parabolic

1. Mpira umakankhidwa mmwamba pa ngodya 60^o motsutsana ndi pamwamba pa bwalo ndi liwiro loyamba la 16 m/s. Kodi mpirawo umayenda mtunda wotani mopingasa? Kuthamanga kwa mphamvu yokoka = 10 m/s²
Zokambirana
Amadziwika kuti:
Ngodya (θ) = 60^o
Kecepatan chiyambi (v)_o) = 16 m/s
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa kuti: Mtunda wopingasa (s)
Yankho:
Njira ya mpira ili monga momwe chithunzichi chikusonyezera.
Liwiro loyamba la mpira mbali yopingasa:
v_ox =v_o cos θ = (16 m/s)(cos 60^o) = (16 m/s)(0,5) = 8 m/s
Liwiro loyamba la mpira mbali yowongoka:
v_oy =v_o uchimo θ = (16 m/s)(uchimo 60^o) = (16 m/s)(0,5√3) = 8√3 m/s

Kuyenda kwa parabolic ndi kuphatikiza kwa kuyenda kolunjika ndi kolunjika. Chifukwa chake, kuyenda kwa parabolic kumasanthulidwa ngati kuti kwapangidwa ndi mayendedwe awiri osiyana. Kuyenda kolunjika kumasanthulidwa ngati kuyenda kolunjika kofanana , ndipo kuyenda kolunjika kumasanthulidwa ngati kuyenda kolunjika mmwamba.

Nthawi yopumira mpira mlengalenga
Choyamba, werengerani nthawi yomwe mpira uyenera kuyenda mu parabola. Nthawi yomwe ikugwiritsidwa ntchito imawerengedwa pogwiritsa ntchito njira yoyendetsera molunjika mmwamba.
Pothetsa vuto la kuyenda molunjika mmwamba, kuchuluka kwa vekitala Vekitala yomwe imayang'ana mmwamba imapatsidwa chizindikiro chabwino, vekitala yomwe imayang'ana pansi imapatsidwa chizindikiro choipa.
Amadziwika kuti:
Liwiro loyambirira (v)_o) = 8√3 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)
Kutalika (h) = 0 (mpira ukabwerera pamalo ake oyamba, kusintha kwa kutalika kwa mpirawo ndi zero)
Anafunsa kuti: Nthawi yopuma (t) yomwe mpira umayenda motsatira parabola
Yankho:
Zikudziwika kuti v_o, g, h ndipo anafunsa t kotero kuti njira yoyendetsera moyimirira mmwamba yomwe imagwiritsidwa ntchito ndi h = v_o t + 1/2 gt²

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

Mtunda wopingasa womwe mpira umafikira
Mtunda wopingasa umawerengedwa pogwiritsa ntchito njira yofanana yoyendera mzere.
Amadziwika kuti:
Liwiro (v) = 8 m/s
Nthawi yopuma (t) = masekondi 2,8
Anafunsa kuti: Jarak
Yankho:
s = vt = (8 m/s)(2,8 s) = mamita 22,4

Mtunda wopingasa womwe mpira umafikira ndi mamita 22,4.

2. Chipolopolocho chimawomberedwa mmwamba pa ngodya ya 60°^o mopingasa kuchokera pamalo okwana mamita 50 kuchokera pansi. Liwiro loyamba la chipolopolo ndi 30 m/s. Werengani mtunda waukulu kwambiri womwe chipolopolocho chimafikira! Kuthamanga chifukwa cha mphamvu yokoka ndi 10 m/s²
Zokambirana
Amadziwika kuti:
Ngodya (θ) = 60^o
Kutalika (h) = 15 m
Liwiro loyambirira (v)_o) = 30 m/s
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa kuti: mtunda wautali kwambiri womwe chipolopolo chimafikira
Yankho:
Njira ya chipolopolocho ndi monga momwe chithunzichi chikusonyezera.
Liwiro loyamba la mpira mbali yopingasa:
v_ox =v_o cos θ = (30 m/s)(cos 60^o) = (30 m/s)(0,5) = 15 m/s
Liwiro loyamba la mpira mbali yowongoka:
v_oy =v_o uchimo θ = (30 m/s)(uchimo 60^o) = (30 m/s)(0,5√3) = 15√3 m/s

Kutha kwa chipolopolo mumlengalenga nthawi
Choyamba, werengerani nthawi yomwe chipolopolocho chiziyenda mu parabola. Nthawi yomwe chipolopolocho chiziyenda imawerengedwa pogwiritsa ntchito fomula iyi kuyenda koyima 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) = 15√3 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)
Kutalika (h) = -50 (mpira ukafika pansi, uli pamtunda wa mamita 50) ndi bawa malo oyamba kotero kuti ndi oipa)
Anafunsa kuti: Nthawi yopuma (t) yomwe mpira umayenda motsatira parabola
Yankho:
Zikudziwika kuti v_o, g, h ndipo anafunsa t kotero kuti njira yoyendetsera moyimirira mmwamba yomwe imagwiritsidwa ntchito ndi h = v_o t + 1/2 gt²

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

t imawerengedwa pogwiritsa ntchito fomula ya ABC
a = 5, b = -15√3, c = -50

Nthawi yoti mpira upite motsatira parabola ndi masekondi 6,7.

Mtunda wopingasa womwe mpira umafikira
Mtunda wopingasa umawerengedwa pogwiritsa ntchito njira yofanana yoyendera mzere.
Amadziwika kuti:
Liwiro (v) = 15 m/s
Nthawi yopuma (t) = masekondi 6,7
Anafunsa kuti: Jarak
Yankho:
s = vt = (15 m/s)(6,7 s) = mamita 100,5

Mtunda wopingasa womwe mpira umafikira ndi mamita 100,5.

3. Marble imaponyedwa mopingasa kumanja kuchokera kutalika kwa mamita 10 ndi liwiro loyambirira la 10 m/s. Dziwani mtunda wopingasa womwe marble imafikira! Kuthamanga chifukwa cha mphamvu yokoka = 10 m/s²
Zokambirana
Amadziwika kuti:
Kutalika (h) = 10 m
Liwiro loyambirira (v)_o) = 10 m/s
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Anafunsa kuti: mtunda wopingasa womwe umafikiridwa ndi miyala ya marble
Yankho:
Njira ya miyala ya marble ili monga momwe yasonyezedwera pachithunzichi.
Liwiro loyambirira mbali yopingasa = liwiro loyambirira = 10 m/s

Nthawi ya marble mumlengalenga
Choyamba, werengerani nthawi yomwe mpira uyenera kuyenda motsatira parabola. Nthawi yomwe imachitika imawerengedwa pogwiritsa ntchito fomula iyi kuyenda kwaulere kwa kugwa.
Amadziwika kuti:
Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²
Kutalika (h) = mamita 10
Anafunsa kuti: Nthawi yopuma (t) yomwe mpira umayenda motsatira parabola
Yankho:
Popeza g, h ndi asked t kotero fomula yoyendetsera yomasuka 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

Mtunda wopingasa womwe umafikiridwa ndi miyala ya marble
Mtunda wopingasa umawerengedwa pogwiritsa ntchito njira yofanana yoyendera mzere.
Amadziwika kuti:
Liwiro (v) = 10 m/s
Nthawi yopuma (t) = masekondi 1,4
Anafunsa kuti: Jarak
Yankho:
s = vt = (10 m/s)(1,4 s) = mamita 14

Mtunda wopingasa womwe umafikiridwa ndi miyala ya marble ndi mamita 14.

[Chingerezi: Kuthetsa mavuto oyenda ndi zombo - kudziwa kusuntha kopingasa ]