Misali na tambaya don tantance nisan da ke tsakanin motsin parabolic

Misalai 3 na tambayoyi don tantance nisan da ke tsakanin motsin parabolic

1. An harba ƙwallon sama a kusurwar 60^o a saman filin da saurin farko na m16/s. Wane nisa a kwance ƙwallon ke tafiya? Haɓaka nauyi = 10m/s²
Tattaunawa
An san cewa:
Kusurwoyi (θ) = 60^o
Kecepatan farawa (v)_o) = 16 m/s
Saurin gudu saboda nauyi (g) = 10 m/s²
An tambaya: Nisa a kwance (s)
Amsa:
Hanyar ƙwallon kamar yadda aka nuna a hoton.
Saurin farko na ƙwallon a cikin alkiblar kwance:
v_ox = v_o cos θ = (16 m/s)(cos 60^o) = (16 m/s)(0,5) = 8 m/s
Saurin farko na ƙwallon a tsaye:
v_oy = v_o zunubi θ = (16 m/s)(zunubi 60^o) = (16 m/s)(0,5√3) = 8√3 m/s

Motsin Parabolic haɗuwa ce ta motsi a kwance da a tsaye. Saboda haka, ana nazarin motsin parabolic kamar an haɗa shi da motsi biyu daban-daban. Ana nazarin motsin kwance a matsayin motsi na layi ɗaya , kuma ana nazarin motsi na tsaye a matsayin motsi na tsaye sama.

Tazarar lokaci na ƙwallon a cikin iska
Da farko, a ƙididdige tazarar lokacin da ƙwallon za ta motsa a cikin parabola. Ana ƙididdige tazarar lokacin ta amfani da dabarar motsi sama a tsaye.
Wajen magance matsalar motsi a tsaye sama, Adadin vector Ana ba wa vector wanda alkiblarsa ta kai sama alama mai kyau, vector wanda alkiblarsa ta kai ƙasa alama mai korau.
An san cewa:
Saurin farko (v)_o) = 8√3 m/s (mai kyau saboda alkiblar saurin farko yana sama)
Saurin gudu saboda nauyi (g) = -10 m/s² (mara kyau saboda alkiblar saurin nauyi tana ƙasa)
Tsawo (h) = 0 (lokacin da ƙwallon ta koma matsayinta na asali, canjin tsayin ƙwallon sifili ne)
An tambaya: Tazarar lokaci (t) da ƙwallon ke motsawa tare da parabola
Amsa:
An san cewa v_o, g, h kuma an nemi t domin dabarar motsi a tsaye sama da aka yi amfani da ita ita ce 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 = 5t
t = 14 / 5 = daƙiƙa 2,8

Nisa a kwance da ƙwallon ta kai
Ana ƙididdige nisan kwance ta amfani da dabarar motsi mai layi ɗaya.
An san cewa:
Gudun (v) = 8 m/s
Tazarar lokaci (t) = daƙiƙa 2,8
An tambaya: Nisa
Amsa:
s = vt = (8 m/s)(2,8 s) = mita 22,4

Nisa a kwance da ƙwallon ta kai mita 22,4.

2. Ana harba harsashin sama a kusurwar 60°^o a kwance daga wani wuri mai nisan mita 50 sama da matakin ƙasa. Saurin farko na harsashin shine m30/s. Lissafa mafi girman nisan da harsashin zai kai! Saurin da harsashin ke yi saboda nauyi shine m10/s²
Tattaunawa
An san cewa:
Kusurwoyi (θ) = 60^o
Tsawo (h) = mita 15
Saurin farko (v)_o) = 30 m/s
Saurin gudu saboda nauyi (g) = 10 m/s²
An tambaya: nisan da harsashi ya kai
Amsa:
Hanyar harsashin kamar yadda aka nuna a hoton.
Saurin farko na ƙwallon a cikin alkiblar kwance:
v_ox = v_o cos θ = (30 m/s)(cos 60^o) = (30 m/s)(0,5) = 15 m/s
Saurin farko na ƙwallon a tsaye:
v_oy = v_o zunubi θ = (30 m/s)(zunubi 60^o) = (30 m/s)(0,5√3) = 15√3 m/s

Lokacin da harsashi ya faɗi a sama
Da farko, ƙididdige tazarar lokacin da harsashi zai motsa a cikin parabola. Ana ƙididdige tazarar lokacin ta amfani da dabarar. motsi a tsaye sama.
A wajen magance matsaloli a kan motsi a tsaye sama, adadin vektor da aka nuna sama ana ba shi alama mai kyau, adadin vektor da aka nuna ƙasa ana ba shi alama mara kyau.
An san cewa:
Saurin farko (v)_o) = 15√3 m/s (mai kyau saboda alkiblar saurin farko yana sama)
Saurin gudu saboda nauyi (g) = -10 m/s² (mara kyau saboda alkiblar saurin nauyi tana ƙasa)
Tsawo (h) = -50 (idan ya isa ƙasa, ƙwallon tana da nisan mita 50) karkashin matsayin farko don haka yana da korau)
An tambaya: Tazarar lokaci (t) da ƙwallon ke motsawa tare da parabola
Amsa:
An san cewa v_o, g, h kuma an nemi t domin dabarar motsi a tsaye sama da aka yi amfani da ita ita ce 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

Ana ƙididdige t ta amfani da dabarar ABC
a = 5, b = -15√3, c = -50

Tazarar lokaci (t) don ƙwallon ya motsa tare da parabola shine daƙiƙa 6,7.

Nisa a kwance da ƙwallon ta kai
Ana ƙididdige nisan kwance ta amfani da dabarar motsi mai layi ɗaya.
An san cewa:
Gudun (v) = 15 m/s
Tazarar lokaci (t) = daƙiƙa 6,7
An tambaya: Nisa
Amsa:
s = vt = (15 m/s)(6,7 s) = mita 100,5

Nisa a kwance da ƙwallon ta kai mita 100,5.

3. Ana jefa marmara a kwance zuwa dama daga tsayin mita 10 tare da saurin farko na mita 10/s. Kayyade nisan kwance da marmarar ta kai! Saurin gudu saboda nauyi = mita 10/s²
Tattaunawa
An san cewa:
Tsawo (h) = mita 10
Saurin farko (v)_o) = 10 m/s
Saurin gudu saboda nauyi (g) = 10 m/s²
An tambaya: Nisa a kwance da marmara ta isa
Amsa:
Hanyar marmara kamar yadda aka nuna a hoton.
Saurin farko a cikin alkiblar kwance = saurin farko = 10 m/s

Tazarar lokaci na marmara a cikin iska
Da farko, a ƙididdige tazarar lokacin da ƙwallon za ta motsa tare da parabola. Ana ƙididdige tazarar lokacin ta amfani da dabarar. motsi na faɗuwa kyauta.
An san cewa:
Saurin gudu saboda nauyi (g) = 10 m/s²
Tsawo (h) = mita 10
An tambaya: Tazarar lokaci (t) da ƙwallon ke motsawa tare da parabola
Amsa:
An ba da g, h kuma an nemi t don haka dabarar motsi na faɗuwa kyauta da aka yi amfani da ita ita ce h = 1/2 gt²
h = 1/2 gt²
10 = 1/2 (10) t²
10 = 5t²
t² = 10/5 = 2
t = √2 = daƙiƙa 1,4

Nisa a kwance da marmara ta isa
Ana ƙididdige nisan kwance ta amfani da dabarar motsi mai layi ɗaya.
An san cewa:
Gudun (v) = 10 m/s
Tazarar lokaci (t) = daƙiƙa 1,4
An tambaya: Nisa
Amsa:
s = vt = (10 m/s)(1,4 s) = mita 14

Nisa a kwance da marmara ta isa ita ce mita 14.

[Turanci: Magance matsalolin motsin harsashi - tantance ƙaura a kwance ]