Misalai 4 na tambayoyi don tantance tazara tsakanin lokacin motsi na parabolic
1. An harba ƙwallon sama a kusurwar 30o a saman filin da saurin farko na m10/s. Ka ƙayyade tazarar lokacin da ƙwallon za ta kai matsakaicin tsayinta! Haɓaka nauyi = 10m/s2
Tattaunawa
An san cewa:
Kusurwoyi (θ) = 30o
Kecepatan farawa (v)o) = 10 m/s
Saurin gudu saboda nauyi (g) = 10 m/s2
An tambaya: Tazarar lokacin da ƙwallon zai kai ga matsakaicin tsayinsa
Amsa:
Saurin farko na ƙwallon a tsaye:
voy = vo zunubi θ = (10 m/s)(zunubi 30o) = (10 m/s)(0,5) = 5 m/s
Ana ƙididdige tazarar lokacin da ƙwallon zai kai matsakaicin tsayinsa ta amfani da dabarar motsi a tsaye sama.
Wajen magance matsalolin da suka shafi motsi a tsaye sama, adadin vektor da aka tura sama ana ba shi alama mai kyau, Adadin vector alkiblar ƙasa an ba ta alama mara kyau.
An san cewa:
Saurin farko (v)o) = 5 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)
Saurin ƙarshe (v)t) = 0 (a matsakaicin tsayi, abin yana nan na ɗan lokaci kafin ya canza alkibla)
An tambaya: Tazarar lokaci (t)
Amsa:
An san cewa vo, g da vt, an tambayi t don haka ana amfani da dabarar vt = vo + gt
vt = vo + gt
0 = 5 + (-10)t
0 = 5 – 10 t
5 = 10t
t = 5/10 = daƙiƙa 0,5
Tsawon lokacin da ƙwallon zai kai ga matsakaicin tsayinsa shine daƙiƙa 0,5.
2. An jefa ƙwallon sama a kusurwar 30o a kwance tare da saurin farko na m 8/s. Tsawon lokacin da ƙwallon zai ɗauka kafin ta isamotsin parabolic! Saurin gudu saboda nauyi = 10 m/s2
Tattaunawa
An san cewa:
Kusurwoyi (θ) = 30o
Saurin farko (v)o) = 8 m/s
Saurin gudu saboda nauyi (g) = 10 m/s2
An tambaya: Lokacin da ƙwallon zai motsa a cikin parabola
Amsa:
Saurin farko na ƙwallon a tsaye:
voy = vo zunubi θ = (8 m/s)(zunubi 30o) = (8 m/s)(0,5) = 4 m/s
Da farko, ƙididdige tazarar lokacin da abu zai kai ga matsakaicin tsayinsa 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) = 4 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)
Saurin ƙarshe (v)t) = 0 (a matsakaicin tsayi, abin yana nan na ɗan lokaci kafin ya canza alkibla)
An tambaya: Tazarar lokaci (t)
Amsa:
An san cewa vo, g da vt, an tambayi t don haka ana amfani da dabarar vt = vo + gt
vt = vo + gt
0 = 4 + (-10)t
0 = 4 – 10 t
4 = 10t
t = 4/10 = daƙiƙa 0,4
Tsawon lokacin da ƙwallon zai kai ga matsakaicin tsayinsa shine daƙiƙa 0,4.
Hanyar ƙwallon tana da daidaito, don haka tazarar lokacin da ƙwallon za ta motsa sama iri ɗaya ne da tazarar lokacin da ƙwallon za ta motsa ƙasa. Don haka jimlar tazarar lokaci shine daƙiƙa 2 x 0,4 = daƙiƙa 0,8.
3. Ana harba harsashin sama a kusurwar 30°o a kwance daga wani wuri mai nisan mita 10 daga sama da ƙasa. Saurin farko na harsashin shine m40/s. Tsawon wane lokaci harsashin zai ɗauka kafin ya isa ƙasa? Saurin da aka samu sakamakon nauyi shine m10/s2
Tattaunawa
An san cewa:
Kusurwoyi (θ) = 30o
Tsawon farko (h)o) = mita 10
Saurin farko (v)o) = 40 m/s
Saurin gudu saboda nauyi (g) = 10 m/s2
An tambaya: Lokacin da harsashin ya faɗi a sararin sama
Amsa:
Saurin farko na ƙwallon a tsaye:
voy = vo zunubi θ = (40 m/s)(zunubi 30o) = (40 m/s)(0,5) = 20 m/s
Da farko, ƙididdige tazarar lokacin da harsashin zai kai ga matsakaicin tsayinsa 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) = 20 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)
Saurin ƙarshe (v)t) = 0 (a matsakaicin tsayi, abin yana nan na ɗan lokaci kafin ya canza alkibla)
An tambaya: Tazarar lokaci (t)
Amsa:
An san cewa vo, g da vt, an tambayi t don haka ana amfani da dabarar vt = vo + gt
vt = vo + gt
0 = 20 + (-10)t
0 = 20 – 10 t
20 = 10t
t = 20/10 = daƙiƙa 2
Tsawon lokacin da ƙwallon zai kai ga matsakaicin tsayinsa shine daƙiƙa 2.
Hanyar ƙwallon tana da daidaito, don haka tazarar lokacin da ƙwallon ke cikin iska shine daƙiƙa 2 x 2 = daƙiƙa 4.
An harba harsashi daga wani wuri mai nisan mita 10 daga ƙasa. Yana ɗaukar daƙiƙa 4 kafin ƙwallon ta isa wurin farawa. Ƙwallon ta ci gaba da tafiya ƙasa.
Ana ƙididdige tazarar lokacin da ƙwallon zai sauka daga tsayin mita 10 ne domin tantance tazarar lokacin da za a yi amfani da shi wajen faɗuwa kyauta.
An san cewa:
Saurin gudu saboda nauyi (g) = 10 m/s2
Tsawo (h) = mita 10
An tambaya: Tazarar lokaci (t)
Amsa:
An ba da g, h kuma an nemi t don haka dabarar motsi ta 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
Lokacin da harsashi zai faɗo daga tsayin mita 10 shine daƙiƙa 1,4.
Jimillar lokacin da harsashin ya yi sama da daƙiƙa 4 + daƙiƙa 1,4 = daƙiƙa 5,4.
4. Ana jefa marmara a kwance zuwa dama daga tsayin mita 5 tare da saurin farko na mita 15/s. Ka ƙayyade tazarar lokacin da marmarar take cikin iska! Saurin gudu saboda nauyi = 10 m/s2
Tattaunawa
An san cewa:
Tsawo (h) = mita 5
Saurin farko (v)o) = 15 m/s
Saurin gudu saboda nauyi (g) = 10 m/s2
An tambaya: Lokacin da marmara ke cikin iska
Amsa:
Hanyar da marmarar take tafiya kamar yadda aka nuna a hoton. An ƙididdige tazarar lokacin da marmarar ke cikin iska ta amfani da dabarar. motsi na faɗuwa kyauta.
An san cewa:
Tsawo (h) = mita 5
Saurin gudu saboda nauyi (g) = 10 m/s2
An tambaya: Tazarar lokaci (t)
Amsa:
An ba da g, h kuma an nemi t don haka dabarar motsi ta faɗuwa kyauta da aka yi amfani da ita ita ce h = 1/2 gt2
h = 1/2 gt2
5 = 1/2 (10) t2
5 = 5t2
t2 = 5/5 = 1
t = √1 = daƙiƙa 1
Lokacin da harsashi zai faɗo daga tsayin mita 5 shine daƙiƙa 1.
[Turanci: Magance matsalolin motsin harsashi - ƙayyade tazara tsakanin lokaci]
