Misalai 3 na tambayoyi kan tantance matsayin wani abu da ke motsi a cikin parabola
1. An jefa ƙwallon sama a kusurwar 60o a kwance tare da saurin farko na m12/s. Kayyade matsayin abin bayan motsi na daƙiƙa 1! Haɓaka nauyi = 10m/s2
Tattaunawa
An san cewa:
Kusurwoyi (θ) = 60o
Kecepatan farawa (v)o) = 12 m/s
Tazarar lokaci (t) = daƙiƙa 1
Saurin gudu saboda nauyi (g) = 10 m/s2
An tambaya: Matsayin ƙwallon bayan motsi na daƙiƙa 1
Amsa:
Da farko, ƙididdige abubuwan da suka fara saurin ƙwallon a cikin kwatancen kwance da tsaye.
Saurin farko na ƙwallon a cikin alkiblar kwance:
vox = vo cos θ = (12 m/s)(cos 60o) = (12 m/s)(0,5) = 6 m/s
Saurin farko na ƙwallon a tsaye:
voy = vo zunubi θ = (12 m/s)(zunubi 60o) = (12 m/s)(0,5√3) = 6√3 m/s
Ana ɗaukar motsin parabolic a matsayin haɗin motsi na kwance da tsaye. Ana nazarin motsi na kwance kamar haka: motsi na layi ɗaya, yayin da ake nazarin motsi a tsaye kamar yadda motsi a tsaye samaAna ƙididdige matsayin abu a cikin alkiblar kwance kamar tantance nisan abu da ke tafiya a cikin layi madaidaiciya a cikin ƙimar da ba ta canzawa ba, akasin haka, matsayin abu a cikin alkiblar tsaye ana ƙididdige shi kamar tantance tsayin abu da ke tafiya a tsaye sama.
Matsayin ƙwallon a kwance:
An san cewa:
Saurin ƙwallon a kwance (v)x) = 6 m/s
A cikin motsi madaidaiciya iri ɗaya, saurin abu yana da daidaito don haka saurin farko na abu yayi daidai da saurin abu.
Tazarar lokaci (t) = daƙiƙa 1
An tambaya: Nisa daga abubuwa
Amsa:
Gudun mita 6 a kowace daƙiƙa yana nufin ƙwallon yana motsawa mita 6 a kowace daƙiƙa. Nisa da ƙwallon ke tafiya bayan daƙiƙa 1 mita 6 ne. Saboda haka, matsayin kwance na ƙwallon mita 6 ne.
Matsayin ƙwallon 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 na ƙwallon (v)o) = 6√3 m/s (mai kyau saboda alkiblar saurin farko yana sama)
Tazarar lokaci (t) = daƙiƙa 1
Saurin gudu saboda nauyi (g) = -10 m/s2 (mara kyau saboda saurin nauyi yana ƙasa zuwa tsakiyar duniya)
An tambaya: Tsawon ƙwallon bayan motsi na daƙiƙa 1 (h)
Amsa:
An san cewa vo, t, g kuma an tambayi h don haka dabarar da aka yi amfani da ita ita ce h = vo t + 1/2 gt2
h = vo t + 1/2 gt2 = (6√3)(1) + 1/2 (-10)(1)2) = 6√3 + (-5)(1) = 6√3 – 5 = 6(1,7) – 5 = 10,2 – 5 = mita 5,2.
Matsayin ƙwallon bayan motsi na daƙiƙa 1:
Matsayin ƙwallon a kwance (x) = mita 6
Matsayin ƙwallon a tsaye (y) = mita 5,2
Don haka daidaitattun matsayin ƙwallon sune (x; y) = (6; 5,2)
2. Ana harba harsashin sama a kusurwar 30°o a kwance daga wani wuri mai nisan mita 20 daga matakin ƙasa. Saurin farko na harsashin shine m50/s. Har yaushe harsashin zai kai bayan ya motsa na daƙiƙa 1? Saurin da aka samu sakamakon nauyi shine m10/s2
Tattaunawa
An san cewa:
Kusurwoyi (θ) = 30o
Tsawon farko na harsashi (h)o) = mita 20
Saurin farko na harsashi (v)o) = 50 m/s
Tazarar lokaci (t) = daƙiƙa 1
Saurin gudu saboda nauyi (g) = 10 m/s2
An tambaya: Tsawon harsashi
Amsa:
Saurin farko na harsashi a tsaye:
Da farko, ƙididdige ɓangaren saurin farko na ƙwallon a tsaye.
voy = vo zunubi θ = (50 m/s)(zunubi 30o) = (50 m/s)(0,5) = 25 m/s
Tsawon harsashi:
An ƙididdige tsayin harsashin ne a matsayin tantance tsayin da ake so a 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 na harsashi (v)o) = 25 m/s (mai kyau saboda alkiblar saurin farko yana sama)
Tazarar lokaci (t) = daƙiƙa 1
Saurin gudu saboda nauyi (g) = -10 m/s2 (mara kyau saboda alkiblar saurin nauyi tana ƙasa zuwa tsakiyar duniya)
An tambaya: Tsawon harsashi (h)
Amsa:
An san cewa vo, t, g kuma an tambayi h don haka dabarar da aka yi amfani da ita ita ce h = vo t + 1/2 gt2
h = vo t + 1/2 gt2 = (25)(1) + 1/2 (-10)(1)2) = 25 + (-5)(1) = 25 – 5 = mita 20.
Tsawon harsashin bayan ya yi motsi na daƙiƙa 1 yana da mita 20 a sama inda harsashin ya yi ko kuma mita 40 a sama da matakin ƙasa.
3. Ana jefa marmara a kwance zuwa dama daga tsayin mita 10 tare da saurin farko na m10/s. A tantance matsayin marmarar bayan an motsa na daƙiƙa 1! Saurin gudu saboda nauyi = m10/s2
Tattaunawa
An san cewa:
Tsawon farko (h) = mita 10
Saurin farko (v)o) = 10 m/s
Tazarar lokaci (t) = daƙiƙa 1
Saurin gudu saboda nauyi (g) = 10 m/s2
An tambaya: Matsayin marmara bayan motsi na daƙiƙa 1
Amsa:
Hanyar marmara kamar yadda aka nuna a hoton. Idan hanyar tana da kama da juna kamar yadda aka nuna a hoton, ana tantance matsayin abin a tsaye kamar lissafin tsayin da ke cikin faɗuwar 'free fall', yayin da matsayin abin a kwance ana tantance shi kamar lissafin nisa a cikin motsi madaidaiciya iri ɗaya.
Da farko, marmarar tana motsawa a kwance ta yadda saurin farko na marmarar a kwance (v)ox) shine 10 m/s, yayin da saurin farko na marmara a tsaye (voy(0 m/s) shine 0 m/s.
Matsayin marmara a cikin shugabanci na kwance:
An san cewa:
Saurin marmara a cikin alkiblar kwance (v)x) = 10 m/s
A cikin motsi madaidaiciya iri ɗaya, saurin abu yana da daidaito don haka saurin farko na abu yayi daidai da saurin abu.
Tazarar lokaci (t) = daƙiƙa 1
An tambaya: Nisa daga abubuwa
Amsa:
Gudun mita 10 a kowace daƙiƙa yana nufin cewa marmarar tana tafiya mita 10 a kowace daƙiƙa. Nisa da marmarar ke tafiya bayan ta yi tafiya na daƙiƙa 1 shine mita 10. Saboda haka, matsayin marmarar a kwance shine mita 10.
Matsayin marmara a tsaye:
An yi nazari kamar yadda motsi na faɗuwa kyauta.
An san cewa:
Tazarar lokaci (t) = daƙiƙa 1
Saurin gudu saboda nauyi (g) = 10 m/s2
An tambaya: Tsayin marmara bayan motsi na daƙiƙa 1 (h)
Amsa:
Idan aka ba da t, g kuma aka nemi h don haka dabarar da aka yi amfani da ita ita ce h = 1/2 gt2
h = 1/2 gt2 = 1/2 (10)(1)2) = (5)(1) = mita 5.
Bayan daƙiƙa 1, marmarar ta faɗi mita 5. Tsawon marmarar da ke sama da ƙasa mita 10 – mita 5 = mita 5.
Matsayin marmara bayan motsi na daƙiƙa 1:
Matsayin marmara a kwance (x) = mita 10
Matsayin marmara a tsaye (y) = mita 5
Don haka daidaitattun matsayin marmara sune (x; y) = (10; 5)
[Turanci: Magance matsalolin motsin harsashi - tantance matsayin abu]
