27 Motsin da ke fitowa daga jirgin sama - matsaloli da mafita
1. Ana harba harsashi a kusurwa θ = 60 o tare da saurin mita 20/s. Saurin da aka samu sakamakon nauyi shine 10 m/s 2. Menene tazarar lokacin da za a kai ga matsakaicin tsayi?
An sani:
Saurin farko na harsashi (v o ) = 20 m/s
Kusurwoyi (θ) = 60 o C
Saurin gudu saboda nauyi (g) = 10 ms –2
Ana so: Tazarar lokaci don isa ga matsakaicin tsayi
Magani:
Saurin farko a alkiblar kwance (axis x):
v ox = v o cos 60 o = (20) (0.5) = 10 m/s
Saurin farko a tsaye (axis y):
v oy = vo sin 60 o = (20)(0.5√3) = 10√3 m/s
Tazarar lokaci don isa ga matsakaicin tsayi, wanda aka ƙididdige ta amfani da wannan lissafi:
v ty = v oy + gt
v ty = gudun ƙarshe a tsaye = gudun ƙarshe a mafi girman matsayi = 0 m/s
v oy = saurin farko a kusurwar kwance = 10√3 m/s
g = hanzari saboda nauyi = 10 m/s 2
t = tazara tsakanin lokaci
Tazarar lokaci:
v ty = v oy + gt
0 = 10√3 – 10 t
10√3 = t 10
t = 10√3 / 10
t = √ daƙiƙa 3
2. Wani abu da aka zana a kusurwa. Tsawon abin iri ɗaya ne idan tazarar lokaci = daƙiƙa 1 da daƙiƙa 3. Menene tazarar lokacin abu a cikin iska.
Magani:
Abu a cikin iska na tsawon daƙiƙa 4.
3. Jirgin sama yana tafiya a kwance tare da gudun mita 50/s. A tsayin kilomita 2, ana sauke wani abu daga jirgin. Saurin gudu saboda nauyi = 10 m/ s2, menene tazara tsakanin lokacin da abin ya kai ƙasa.
An sani:
Tsawo = 2 km = mita 2000
Saurin gudu saboda nauyi (g) = 10 m/s 2
Ana so: Tazarar lokaci (t)
Magani:
h = 1/2 gt 2
2000 = 1/2 (10) t 2
2000 = 5 t 2
t 2 = 2000/5 = 400
t = √400 = daƙiƙa 20
4. Ƙwallon ƙafa da aka harba ta bar ƙasa a kusurwa θ = 45 o tare da kwance yana da saurin farko na 25 m/s. Kayyade nisan X. Hanzari saboda nauyi shine 10 m/s 2.
An sani:
Saurin farko (v o ) = 25 m/s
Saurin gudu saboda nauyi (g) = 10 m/s 2
Kusurwoyi (θ) = 45 o
Ana so: X
Magani:
Bangaren kwance na saurin farko:
v ox = v o cos θ = (25m/s)(cos 45 o ) = (25m/s)(0.5√2) = 12.5√2 m/s
Bangaren tsaye na saurin farko:
v oy = v o sin θ = (25m/s)(sin 45 o ) = (25m/s)(0.5√2) = 12.5√2 m/s
Ana iya fahimtar motsin da aka yi ta hanyar nazarin sassan motsi na kwance da tsaye daban-daban. Motsin x yana faruwa ne a saurin da ba ya canzawa, kuma motsin y yana faruwa ne a saurin nauyi akai-akai.
Ana ƙididdige lokacin da ake amfani da shi a iska ta hanyar lissafin motsin tsaye sama.
Zaɓi hanyar sama a matsayin mai kyau, kuma hanyar ƙasa a matsayin mara kyau.
An sani:
Saurin farko (v o ) = 12.5√2 m/s (alkiblar sama, tabbatacce)
Saurin gudu saboda nauyi (g) = -10 m/s 2 (alkiblar ƙasa, korau)
Tsawo (h) = 0
Ana so: Tazarar lokaci (t)
Magani:
h = v o t + 1/2 gt 2
0 = (12.5√2) t + 1/2 (-10) t 2
0 = 12.5√2 t – 5 t 2
12.5√2 t = 5 t 2
12.5√2 = t 5
t = 12.5√2 / 5
t = 2.5√ daƙiƙa 2
Nisa a kwance (X):
An ƙididdige ta amfani da lissafin motsi na layi ɗaya tare da saurin da ba ya canzawa.
An sani:
Gudun (v) = 12.5√2 m/s
Tazarar lokaci (t) = 2.5√2 daƙiƙa
Ana nema: Nisa
Magani:
d = vt = (12.5√2)(2.5√2) = (12.5)(2.5)(2) = mita 62.5
5. Wani abu da aka haska sama a kusurwa θ = 30 o tare da kwance yana da saurin farko na 20 m/s. Saurin da aka samu saboda nauyi shine 10 m/s 2. Kayyade matsakaicin tsayi.
An sani:
Saurin farko (v)o) = 20 m/s
Saurin gudu saboda nauyi (g) = 10 m/s 2
Kusurwoyi (θ) = 30 o
Ana so : Matsakaicin tsayi
Magani:
Da farko, nemo bangaren tsaye na saurin farko (v oy ):
v oy = v o zunubi 30 o = (20)(zunubi 30 o ) = (20) (0.5) = 10 m/s
A ƙididdige matsakaicin tsayi. Zaɓi hanyar sama a matsayin mai kyau da kuma hanyar ƙasa a matsayin mara kyau.
An sani:
Saurin gudu saboda nauyi (g) = -10 m/s 2 ( alkiblar ƙasa , korau )
Bangaren tsaye na saurin farko (v oy ) = 10 m/s ( alkiblar sama, mai kyau )
Gudun da ke kan matsakaicin tsayi (v ty ) = 0
Ana so: Matsakaicin tsayi (h)
Magani:
v t 2 = v o 2 + 2 gh
0 2 = 10 2 + 2 (-10) h
0 = 100 – 20 hours
100 = awanni 20
h = 100/20
h = mita 5
Tsawon mafi girma shine mita 5.
6. Ana jefa wani abu a wani kusurwar ɗagawa. Tsawon abin iri ɗaya ne bayan daƙiƙa 1 da daƙiƙa 3. A ƙayyade lokaci a cikin iska.
A. 3.6 s
B. 4.0 s
C. 5.6 s
D. 6.4 s
Magani
Lokacin da ake amfani da shi a iska = daƙiƙa 4.
Amsar da ta dace ita ce B.
7. Jirgin sama yana tafiya a kwance tare da gudun mita 50/s. Idan jirgin sama ya kai tsayin kilomita 2, abu zai iya faɗuwa daga jirgin sama cikin 'yanci. Kayyade nau'in motsi.
A. Motsin faɗuwa kyauta
B. Motsin shawagi
C. Motsin kwance
D. Motsin da ke fitowa daga sama
Magani:
An sauke abin daga jirgin sama mai motsi saboda yana da saurin gudu iri ɗaya da gudun jirgin, wato mita 50/s. Motsin abubuwa ba kamar motsi ne na faɗuwa kyauta ba, amma motsi ne na parabolic. Yanayin yana kama da wanda kake faɗuwa daga cikin motar da ke motsi.
Amsar da ta dace ita ce D.
8. Ana jefa ƙwallon a kwance a gudun mita 15/s daga wani dutse mai tsawon mita 60. Tsawon lokacin da ake ɗauka kafin a faɗi ƙasa?
Magani: Ta amfani da \( h = \frac{1}{2} gt^2 \), mun gano cewa lokacin shine \( t = \sqrt{\frac{2h}{g}} \approx 3.5\ \text{s} \).
9. Ana harba wani harsashi a kusurwar 30° sama da kwance tare da saurin farko na 20 m/s. Menene matsakaicin tsayin da aka kai?
Magani: Ta amfani da \( h = \frac{v^2 \sin^2 \theta}{2g} \), matsakaicin tsayi shine \( h \approx 10.2\ \text{m} \).
10. Ana jefa dutse a kwance a nisan mita 10/s daga hasumiya mai tsayin mita 80. Nemo nisan da yake tafiya a kwance kafin ya faɗi ƙasa.
Magani: Ta amfani da lokacin da aka samu ta hanyar da ta yi kama da Matsala ta 1, nisan kwance shine \( d = vt \approx 40\ \text{m} \).
11. Ana harba bindiga a gudun mita 40/s a kusurwar digiri 45. Nemo lokacin tashi.
Magani: Ta amfani da \( t = \frac{2v \sin \theta}{g} \), lokacin tashi shine \( t \approx 5.8\ \text{s} \).
12. Ana jefa ƙwallon baseball a kusurwar 60° tare da saurin mita 12/s. Nemo kewayon kwance.
Magani: Ta amfani da \( R = \frac{v^2 \sin 2\theta}{g} \), kewayon shine \( R \approx 14.0\ \text{m} \).
13. Ana harba wani makami mai linzami da saurin farko na m 50/s a 37° sama da kwance. Menene bangaren saurin tsaye?
Magani: Bangaren tsaye shine \( v_y = v \sin \theta \approx 30\ \text{m/s} \).
14. Ana harba wani makami a kwance a mita 20/s daga tsayin mita 100. Menene saurin tsaye kafin ya faɗi ƙasa?
Magani: Ta amfani da \( v_y = \sqrt{2gh} \), saurin tsaye shine \( v_y \approx 44.7\ \text{m/s} \).
15. Ana jefa dutse a kusurwar 25° sama da kwance tare da saurin farko na 15 m/s. Menene sassan kwance da tsaye na saurin?
Magani: Bangaren kwance shine \( v_x = v \cos \theta \approx 13.4\ \text{m/s} \), kuma bangaren tsaye shine \( v_y \approx 6.4\ \text{m/s} \).
16. Ana bugun ƙwallon ƙafa da saurin farko na m 30/s a kusurwar 40° sama da kwance. Menene ɓangaren saurinsa na kwance?
Magani: Bangaren kwance shine \( v_x = v \cos \theta \approx 22.9\ \text{m/s} \).
17. Ana bugun ƙwallon golf da saurin farko na m 70/s a kusurwar 20°. Menene lokacin tashi?
Magani: Ta amfani da lissafin lokacin tashi, lokacin shine \( t \approx 4.9\ \text{s} \).
18. Ana harba wani harsashi daga ƙasa da gudun mita 25/s a 53° sama da kwance. Menene farkon ɓangaren saurinsa a tsaye?
Magani: Bangaren tsaye shine \( v_y = v \sin \theta \approx 20\ \text{m/s} \).
19. Ana jefa ƙwallon baseball da saurin farko na m20/s a kusurwar 50°. Menene matsakaicin tsayin?
Magani: Ta amfani da lissafi don matsakaicin tsayi, tsayin shine \( h \approx 15.3 \ \text{m} \).
20. Ana harba harsashi a kwance da gudun mita 200/s daga tsayin mita 10. Tsawon lokacin da ake ɗauka kafin a faɗi ƙasa?
Magani: Ta amfani da lissafin lokaci, lokacin shine \( t \approx 1.4\ \text{s} \).
21. Ana harba bindiga a gudun mita 45/s a kusurwar digiri 30. Nemo zangon.
Magani: Ta amfani da lissafin kewayon, kewayon shine \( R \approx 88.2\ \text{m} \).
22. Ana jefa ƙwallon kwando a kusurwar 75° tare da saurin mita 10/s. Nemo kewayon kwance.
Magani: Ta amfani da lissafin kewayon, kewayon shine \( R \approx 5.3\ \text{m} \).
23. Ana harba wani makami mai linzami da saurin farko na m 30/s a 22° sama da kwance. Menene saurin tsaye kafin ya kai ga ƙasa?
Magani: Ta amfani da lissafin saurin tsaye, saurin tsaye shine \( v_y \approx 11.4\ \text{m/s} \).
24. Ana jefa dutse a kwance a nisan mita 8//s daga hasumiya mai tsayin mita 40. Menene nisan da yake tafiya a kwance?
Magani: Ta amfani da lissafin nisa na kwance, nisan shine \( d \approx 16\ \text{m} \).
25. Ana bugun ƙwallon ƙafa da saurin farko na m12/s a kusurwar 30° sama da kwance. Menene sassan kwance da tsaye na saurin?
Magani: Bangaren kwance shine \( v_x \approx 10.4\ \text{m/s} \), kuma bangaren tsaye shine \( v_y \approx 6\ \text{m/s} \).
26. Ana bugun ƙwallon golf da saurin farko na m 50/s a kusurwar 15°. Menene lokacin tashi?
Magani: Ta amfani da lissafin lokacin tashi, lokacin shine \( t \approx 2.6\ \text{s} \).
27. Ana harba wani harsashi daga ƙasa da gudun m 40/s a 60° sama da kwance. Menene farkon ɓangaren saurin kwancensa?
Magani: Bangaren kwance shine \( v_x = v \cos \theta \approx 20\ \text{m/s} \).
