Dziwani kusamuka kopingasa kwa kayendedwe ka projectile

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