Misali na tambaya don tantance saurin ƙarshe na motsi na parabolic

Misalai 3 na tambayoyi kan tantance saurin ƙarshe na motsi na parabolic

1. An harba ƙwallon sama a kusurwar 30^o a saman filin da saurin farko na m14/s. Nawa gudun ƙarshen ƙwallon idan ya isa saman filin? Haɓaka nauyi = 10m/s²
Tattaunawa
An san cewa:
Kusurwoyi (θ) = 30^o
Saurin farko (v)_o) = 14 m/s
Saurin gudu saboda nauyi (g) = 10 m/s²
An tambaya: Saurin ƙarshe na ƙwallon idan ya isa saman filin wasa
Amsa:
Hanyar ƙwallon kamar yadda aka nuna a hoton.
Sashen kwance na saurin farko na ƙwallon:
v_ox = v_o cos θ = (14 m/s)(cos 30^o) = (14 m/s)(0,5√3) = 7√3 m/s
Bangaren tsaye na saurin farko na ƙwallon:
v_oy = v_o zunubi θ = (14 m/s)(zunubi 30^o) = (14 m/s)(0,5) = 7 m/s

Ana nazarin motsi a cikin alkiblar kwance kamar motsi madaidaiciya iri ɗaya , yayin da ake nazarin motsi a cikin alkiblar tsaye kamar motsi a tsaye sama.

Saurin ƙarshe na ƙwallon a tsaye a alkiblar
Bayan an motsa sama, ƙwallon zai koma ƙasa. Ana ƙididdige saurin ƙwallon na ƙarshe idan ya bugi ƙasa 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) = 7 m/s (mai kyau saboda alkiblar saurin yana sama)
Saurin gudu saboda nauyi (g) = -10 m/s² (mara kyau saboda alkiblar saurin nauyi tana ƙasa)
Tsawo (h) = 0 (ƙwallon ya dawo matsayinsa na asali don haka canjin tsayin sifili ne)
An tambaya: Saurin ƙarshe na ƙwallon (v)_t)
Amsa:
An san cewa v_o, g, h kuma an tambayi v_t don haka dabarar motsi na tsaye sama da aka yi amfani da ita ita ce v_t² = v_o² + 2 gh

v_t² = v_o² + 2 gh = 72 + 2(-10)(0) = 49 – 0 = 49
v_t = √49 = 7 m/s
Za a iya kammala da cewa saurin farko na ƙwallon lokacin da ake motsawa sama iri ɗaya ne da saurin ƙarshe na ƙwallon lokacin da ya isa saman filin.

Saurin ƙarshe na ƙwallon a cikin alkiblar kwance
Saurin kwance na farko shine 7√3 m/s. A cikin motsi na layi ɗaya, saurin yana da daidaito, don haka saurin farko yayi daidai da saurin ƙarshe. Saboda haka, saurin kwance na ƙarshe na ƙwallon shine 7√3 m/s.

Saurin ƙarshe na ƙwallon idan ya isa saman filin wasa
Saurin ƙarshe na ƙwallon shine haɗuwa da saurin ƙarshe a cikin alkiblar kwance da kuma saurin ƙarshe a tsaye.

Idan hanyar motsi tana da kama da ta cikin hoton da ke sama, to saurin farko iri ɗaya ne da saurin ƙarshe.

2. Ana harba harsashin sama a kusurwar 30°^o a kwance daga wani wuri mai nisan mita 5 daga sama da ƙasa. Saurin farko na harsashin shine m10/s. Menene saurin ƙarshe na harsashin lokacin da ya isa ƙasa? Saurin sauri saboda nauyi shine m10/s²
Tattaunawa
An san cewa:
Kusurwoyi (θ) = 30^o
Tsawon farko (h)_o) = mita 5
Saurin farko (v)_o) = 10 m/s
Saurin gudu saboda nauyi (g) = 10 m/s²
An tambaya: Saurin harsashin ƙarshe idan ya isa ƙasa
Amsa:
Sashen kwance na saurin farko na ƙwallon:
v_ox = v_o cos θ = (10 m/s)(cos 30^o) = (10 m/s)(0,5√3) = 5√3 m/s
Bangaren tsaye na saurin farko na ƙwallon:
v_oy = v_o zunubi θ = (10 m/s)(zunubi 30^o) = (10 m/s)(0,5) = 5 m/s

Ana nazarin motsi a cikin alkiblar kwance kamar motsi madaidaiciya iri ɗaya , yayin da ake nazarin motsi a cikin alkiblar tsaye kamar motsi a tsaye sama.

Saurin ƙarshe na harsashi a tsaye a alkiblar
An san cewa:
Saurin farko (v)_o) = 5 m/s (mai kyau saboda alkiblar saurin yana sama)
Saurin gudu saboda nauyi (g) = -10 m/s² (mara kyau saboda alkiblar saurin nauyi tana ƙasa)
Tsawo (h) = -5 m (mara kyau saboda saman ƙasa yana ƙasa da tsayin farko)
An tambaya: Saurin ƙarshe na ƙwallon (v)_t)
Amsa:
An san cewa v_o, g, h kuma an tambayi v_t don haka dabarar motsi na tsaye sama da aka yi amfani da ita ita ce v_t² = v_o² + 2 gh

v_t² = v_o² + 2 gh = 5² + 2(-10)(-5) = 25 + 100 = 125
v_t = √125 m/s

Saurin ƙarshe na harsashi a kwance
Saurin kwance na farko shine 5√3 m/s. A cikin motsi na layi ɗaya, saurin yana da daidaito, don haka saurin farko yayi daidai da saurin ƙarshe. Saboda haka, saurin kwance na ƙarshe na harsashi shine 5√3 m/s.

Saurin harsashin ƙarshe idan ya isa ƙasa
Saurin ƙarshe na harsashin shine haɗuwa da saurin ƙarshe a cikin alkiblar kwance da kuma saurin ƙarshe a tsaye.

3. Ana jefa marmara a kwance zuwa dama daga tsayin mita 12 tare da saurin farko na mita 8/s. Menene saurin ƙarshe na marmarar lokacin da ta faɗi ƙasa? Saurin gudu saboda nauyi = 10 m/s²
Tattaunawa
An san cewa:
Tsawo (h) = mita 12
Saurin farko (v)_o) = 8 m/s
Saurin gudu saboda nauyi (g) = 10 m/s²
An tambaya: Saurin ƙarshe (v)_t) duwatsu masu daraja lokacin da suka faɗi ƙasa
Amsa:
Hanyar marmara kamar yadda aka nuna a hoton.
Saurin farko na ƙwallon a cikin alkiblar kwance:
v_ox = v_o = 8m/s
Saurin farko na ƙwallon a tsaye:
v_oy = 0m/s

Ana nazarin motsi a cikin alkiblar kwance kamar motsi madaidaiciya iri ɗaya , yayin da ake nazarin motsi a cikin alkiblar tsaye kamar motsi na faɗuwa kyauta.

Saurin ƙarshe na marmara a tsaye a shugabanci
Ana ƙididdige saurin ƙarshe ta amfani da dabarar faɗuwar 'free fall'.
An san cewa:
Saurin gudu saboda nauyi (g) = 10 m/s²
Tsawo (h) = mita 12
An tambaya: Saurin ƙarshe (v)_t)
Amsa:
An ba da g, h da kuma an tambayi vt don haka dabarar motsi ta faɗuwa kyauta da aka yi amfani da ita ita ce v_t² = 2 gh
v_t² = 2 gh = 2(10)(12) = 240
v_t = √240 m/s

Saurin ƙarshe na marmara a cikin shugabanci na kwance
Gudun kwance na farko shine 8 m/s. A cikin motsi na layi ɗaya, saurin yana da daidaito, don haka saurin farko yayi daidai da saurin ƙarshe. Saboda haka, saurin kwance na ƙarshe na marmara shine 8 m/s.

Saurin ƙarshe na marmara lokacin da ya isa saman ƙasa
Gudu na ƙarshe na marmara shine haɗuwa da gudu na ƙarshe a cikin alkiblar kwance da kuma gudu na ƙarshe a tsaye.

[Turanci: Magance matsalolin motsin harsashi - tantance saurin ƙarshe ]