Dziwani kusamuka kopingasa kwa kayendedwe ka projectile

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.

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.

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.

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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