Physics

1. Ƙwallon ƙafa da aka harba ta bar ƙasa a kusurwa θ = 30 ^o zuwa kwance tare da saurin farko na 14 m/s. Lissafa saurin ƙarshe kafin ƙwallon ta faɗi ƙasa.

An sani:

Kusurwoyi ( θ ) = 3 0 ^o

Saurin farko (v _o ) = 14 m/s

Saurin nauyi (g) = 10 m/s ²

Ana nema: Saurin ƙarshe kafin ƙwallon ta faɗi ƙasa

Magani:

Sashen kwance na saurin farko:

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:

v _oy = v _o sin θ = (14m/s)(sin 30 ^o ) = (14m/s)(0.5) = 7 m/s

Saurin ƙarshe a tsaye a alkibla

Zaɓi hanyar sama a matsayin mai kyau, kuma hanyar ƙasa a matsayin mara kyau.

An sani:

Saurin farko (v _o ) = 7 m/s (sama mai kyau)

Saurin nauyi (g) = – 10 m/s ² (ƙasa ta ƙasa)

Tsawo (h) = 0 (abin da aka mayar zuwa matsayin farko)

Ana so: Saurin ƙarshe (v _t )

Magani:

v _t ² = v _o ² + 2 gh = 7 ² + 2 (-10) (0) = 49 - 0 = 49

v _t = √49 = 7 m/s

Saurin ƙarshe a kwance a alkibla

Gudun farko a cikin alkiblar kwance shine 7 √ 3 m/s. Gudun yana da daidaito don haka saurin ƙarshe yayi daidai da saurin farko.

Saurin ƙarshe kafin abu ya faɗi ƙasa

2. An haska jiki sama a kusurwar 30 ^o tare da tsayin daka daga gini mita 5. Saurinsa na farko shine m10/s. A lissafta saurin ƙarshe kafin abin ya faɗo ƙasa! Saurin nauyi shine m10/s ².

An sani:

Kusurwoyi ( θ ) = 30 ^o

Tsawon farko (h _o ) = mita 5

Saurin farko (v _o ) = 10 m/s

Saurin nauyi (g) = 10 m/s ²

Ana so: Saurin ƙarshe

Magani:

Sashen kwance na saurin farko:

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:

v _oy = v _o sin θ = (10m/s)(sin 30 ^o ) = (10m/s)(0.5) = 5 m/s

Saurin ƙarshe a tsaye a alkibla

An sani:

Saurin farko (v _o ) = 5 m/s (sama mai kyau)

Saurin nauyi (g) = – 10 m/s ² (ƙasa ta ƙasa)

Tsawo (h) = -5 m ( mara kyau saboda ƙasa tana ƙasa da tsayin farko)

Ana so: Saurin ƙarshe (v _t )

Magani:

v _t ² = v _o ² + 2 gh = 5 ² + 2 (-10) (-5) = 25 + 100 = 125

v _t = √125 m/s

Saurin ƙarshe a kwance a alkibla

Saurin ƙarshe a kwance shine 5 √3 m/s.

Saurin ƙarshe

3. Ana hango ƙaramin ƙwallon a kwance tare da saurin farko v _o = 8 m/s daga gini mai tsayin mita 12. Lissafa saurin ƙarshe kafin ƙwallon ta faɗi ƙasa ! Saurin nauyi shine 10 m/s ²

An sani:

Tsawo (h) = mita 12

Saurin farko (v _o ) = 8 m/s

Saurin nauyi (g) = 10 m/s ²

Ana so: Saurin ƙarshe (v _t )

Magani:

Sashen kwance na saurin farko:

v _ox = v _o = 8 m/s

Bangaren tsaye na saurin farko:

v _oy = 0 m/s

Saurin ƙarshe a tsaye a alkibla

an ƙididdige ta amfani da lissafin motsi na faɗuwa kyauta.

An sani:

Saurin nauyi (g) = 10 m/s ²

Tsawo (h) = mita 12

Ana so: Saurin ƙarshe (v _t )

Magani:

v _t ² = 2 gh = 2(10)(12) = 240

v _t = √240 m/s

Saurin ƙarshe a kwance a alkibla

Gudun farko a alkiblar kwance shine 8 m/s. Gudun yana nan akai-akai don haka saurin farko yayi daidai da saurin ƙarshe. Don haka saurin ƙarshe a alkiblar kwance shine 8 m/s.

Saurin ƙarshe

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[wpdm_package id='536′]

1. Warware saurin farko zuwa sassan kwance da a tsaye
2. Ƙayyade ƙaura a kwance
3. Ƙayyade matsakaicin tsayi
4. Ƙayyade tazarar lokaci
5. Ƙayyade matsayin abin
6. Ƙayyade saurin ƙarshe

Karin bayani

An warware matsalolin da ke cikin motsin harsashi - ƙayyade matsayin abu

1. Ana haska jiki sama a kusurwar 60 ^o zuwa kwance tare da saurin farko na 12 m/s. Kayyade matsayin abin bayan ya motsa na daƙiƙa 1! Saurin nauyi shine 10 m/s ².

An sani:

Kusurwoyi ( θ ) = 60 ^o

Saurin farko (v _o ) = 12 m/s

Tazarar lokaci (t) = daƙiƙa 1

Saurin nauyi (g) = 10 m/s ²

Ana so: Matsayin abu bayan motsi na daƙiƙa 1

Magani:

Sashen kwance na saurin farko:

v _ox = v _o cos θ = (12m/s) (cos 60 ^o ) = (12m/s) (0.5) = 6 m/s

Bangaren tsaye na saurin farko:

v _oy = v _o sin θ = (12m/s)(sin 60 ^o ) = (12m/s)(0.5 √ 3 ) = 6 √ 3 m/s

Matsayin abu a kwance:

An sani:

Sashen kwance na gudu (v _x ) = 6 m/s

Tazarar lokaci (t) = daƙiƙa 1

Ana so: kewayon kwance (x)

Magani:

Mita 6 / daƙiƙa yana nufin ƙwallon yana motsawa har zuwa mita 6 a kowace daƙiƙa 1. Nisa da ƙwallon bayan ya motsa na daƙiƙa 1 shine mita 6. Don haka matsayin ƙwallon a kwance shine mita 6.

Matsayin abu a tsaye:

Zaɓi hanyar sama a matsayin mai kyau, kuma hanyar ƙasa a matsayin mara kyau.

An sani:

Saurin farko (v _o ) = 6 √ 3 m/s (mai kyau sama)

Tazarar lokaci (t) = daƙiƙa 1

Saurin nauyi (g) = -10 m/s ² (ƙasa ta ƙasa)

Ana so: tsayi bayan motsi na daƙiƙa 1

Magani:

h = v_o 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 abu bayan motsi na daƙiƙa 1:

Matsar da aka yi a kwance (x) = mita 6

Matsar tsaye (y) = mita 5.2

[irp]

2. An haska jiki sama a kusurwar 30 ^o zuwa kwance daga gini mai tsayin mita 20. Saurinsa na farko shine m50/s. Lissafa motsi a tsaye bayan jikin ya motsa na daƙiƙa 1! Saurin nauyi shine m10/s ².

An sani:

Kusurwoyi ( θ ) = 30 ^o

Tsawon farko (h _o ) = mita 20

Saurin farko (v _o ) = 50 m/s

Tazarar lokaci (t) = daƙiƙa 1

Saurin nauyi (g) = 1 0 m/s ²

Ana so: Tsawo (h)

Magani:

Bangaren tsaye na saurin farko:

v _oy = v _o sin θ = (50m/s)(sin 30 ^o ) = (50 m/s)(0.5) = 25 m/s

Height:

Zaɓi hanyar sama a matsayin mai kyau, kuma hanyar ƙasa a matsayin mara kyau.

An sani:

Saurin farko (v _o ) = 25 m/s (sama mai kyau)

Tazarar lokaci (t) = daƙiƙa 1

Hanzarta nauyi (g) = -1 0 m/s ² (ƙasa ta ƙasa)

Ana so: Tsawo (h)

Magani:

h = v _o t + 1/2 gt ^{​​​​2} = (25)(1) + 1/2 (-10)(1 ² ) = 25 + (-5)(1) = 25 – 5 = mita 20.

Tsayin jiki bayan ya yi motsi na daƙiƙa 1 yana da mita 20 a sama inda aka hango jikin ko kuma mita 40 a sama da ƙasa.

[irp]

3. Ana hango ƙaramin ƙwallon a kwance tare da saurin farko v _o = 10 m/s daga gini mai tsayin mita 10. Lissafa motsin ƙwallon bayan ya motsa daƙiƙa 1 ! Saurin nauyi shine 10 m/s ²

An sani:

Tsawon farko (h) = mita 10

Saurin farko (v _o ) = 10 m/s

Tazarar lokaci (t) = daƙiƙa 1

Saurin nauyi (g) = 10 m/s ²

Ana nema: Matsayin ƙwallon bayan motsi daƙiƙa 1!

Magani:

Matsar da aka yi a kwance:

An sani:

Sashen kwance na gudu (v _x ) = 10 m/s

Tazarar lokaci (t) = daƙiƙa 1

Ana so: Matsayin abin

Magani:

Mita 10/daƙiƙa yana nufin abin yana motsawa har zuwa mita 10 a kowace daƙiƙa 1. Motsawa bayan motsi na daƙiƙa 1 mita 10 ne. Don haka motsi a kwance mita 10 ne.

Matsar tsaye:

An ƙididdige shi azaman motsi na faɗuwar 'yanci.

An sani:

Tazarar lokaci (t) = daƙiƙa 1

Saurin nauyi (g) = 10 m/s ²

Ana so: Tsawo bayan motsi na daƙiƙa 1 (h)

Magani:

h = 1/2 gt ^{​​​​2} = 1/2 (10)(1 ² ) = (5)(1) = mita 5.

Bayan daƙiƙa 1, abin zai faɗi har zuwa mita 5. Tsayin da ke sama da matakin ƙasa = mita 10 – mita 5 = mita 5.

Matsayin abin bayan motsi na daƙiƙa 1:

Matsayin abin a kwance (x) = mita 10

Matsayin abin a tsaye (y) = mita 5

[irp]

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[wpdm_package id='536′]

1. Warware saurin farko zuwa sassan kwance da a tsaye
2. Ƙayyade ƙaura a kwance
3. Ƙayyade matsakaicin tsayi
4. Ƙayyade tazarar lokaci
5. Ƙayyade matsayin abin
6. Ƙayyade saurin ƙarshe

Karin bayani

An warware matsalolin da ke cikin motsin harsashi - ƙayyade tazara tsakanin lokaci

1. Ƙwallon ƙafa da aka harba ta bar ƙasa a kusurwa θ = 30 ^o zuwa kwance tare da saurin farko na 10 m/s. Lissafa tazarar lokaci don isa ga matsakaicin tsayi! Saurin nauyi shine 10 m/s ².

An sani:

Kusurwoyi (θ) = 3 0 ^o

Saurin farko (v _o ) = 10 m/s

Saurin nauyi (g) = 10 m/s ²

Ana so: Tazarar lokaci don isa ga matsakaicin tsayi

Magani:

Bangaren tsaye na saurin farko:

v _oy = v _o sin θ = (10 m/s) (sin 30 ^o ) = (10 m/s) (0.5) = 5 m/s

Ana ƙayyade tazarar lokaci zuwa ga matsakaicin tsayi ta hanyar lissafin motsi na tsaye . Zaɓi hanyar sama a matsayin mai kyau da kuma hanyar ƙasa a matsayin mara kyau.

An sani:

Saurin farko (v _o ) = 5 m/s (sama mai kyau)

Saurin nauyi (g) = – 10 m/s ² (ƙasa ta ƙasa)

Gudun ƙarshe a matsakaicin tsayi (v _t ) = 0

Ana so: tazara lokaci (t)

Magani:

v _t = v _o + g t

0 = 5 + (-10)t

0 = 5 – 10 t

5 = 10t

t = 5/10 = 0.5 s

[irp]

2. An haska jiki sama a kusurwar 30 ^o zuwa kwance tare da saurin farko na 30 m/s. Lissafa lokacin tashi! Saurin nauyi shine 10 m/s ².

An sani:

Kusurwoyi (θ) = 3 0 ^o

Saurin farko (v _o ) = 8 m/s

Saurin nauyi (g) = 10 m/s ²

Ana so: Tazarar lokaci kafin jiki ya faɗi ƙasa

Magani:

Bangaren tsaye na saurin farko:

v _oy = v _o sin θ = (8 m/s) (sin 30 ^o ) = (8 m/s) (0.5) = 4 m/s

Da farko za mu ƙididdige tazarar lokaci don isa ga matsakaicin tsayi ta amfani da lissafin motsi na tsaye.

Zaɓi hanyar sama a matsayin mai kyau, kuma hanyar ƙasa a matsayin mara kyau.

An sani:

Saurin farko (v _o ) = 4 m/s (sama mai kyau)

Saurin nauyi (g) = – 10 m/s ² (ƙasa ta ƙasa)

Gudu na ƙarshe a matsakaicin tsayi (v _t ) = 0

Ana so: Tazarar lokaci (t)

Magani:

v _t = v _o + g t

0 = 4 + (-10)t

0 = 4 – 10 t

4 = 10t

t = 4/10 = 0,4 s

Tazarar lokaci don isa ga matsakaicin tsayi shine 0.4 s.

Lokacin da ake amfani da shi a iska shine 2 x 0.4 s = 0.8 s.

[irp]

3. Ana haska jiki sama a kusurwar 30 ^o tare da kwance daga gini tsawon mita 10. Saurinsa na farko shine m 40/s. Tsawon lokacin da zai ɗauka jikin ya isa ƙasa? Saurin nauyi shine m 10/s ².

An sani:

Kusurwoyi (θ) = 3 0 ^o

Tsawon farko (h _o ) = mita 10

Saurin farko (v _o ) = 40 m/s

Saurin nauyi (g) = 10 m/s ²

Ana so: Lokacin da ake watsawa (t)

Magani:

Bangaren tsaye na saurin farko:

v _oy = v _o sin θ = (40m/s)(sin 30 ^o ) = (40m/s)(0.5) = 20 m/s

Da farko za mu ƙididdige tazarar lokaci don isa ga matsakaicin tsayi ta amfani da lissafin motsi na tsaye.

Zaɓi hanyar sama a matsayin mai kyau, kuma hanyar ƙasa a matsayin mara kyau.

An sani:

Saurin farko (v _o ) = 20 m/s (sama mai kyau)

Saurin nauyi (g) = – 10 m/s ² (ƙasa ta ƙasa)

Saurin ƙarshe a lokacin kololuwa (v _t ) = 0

Ana so: Tazarar lokaci (t)

Magani:

v _t = v _o + g t

0 = 20 + (-10)t

0 = 20 – 10 t

20 = 10t

t = 20/10 = daƙiƙa 2

Lokacin da ake amfani da shi a iska = daƙiƙa 2 x 2 = daƙiƙa 4.

Abin yana da nisan mita 10 daga ƙasa. Daƙiƙa 4 shine tazara tsakanin lokacin da za a isa wurin da yake daidai da matsayin farko. Har yanzu ƙwallon tana tafiya ƙasa.

Ana ƙididdige tazarar lokacin da za a isa ƙasa ta amfani da lissafin motsi na faɗuwar 'free fall'.

An sani:

Saurin nauyi (g) = 10 m/s ²

Tsawo (h) = mita 10

Ana so: Tazarar lokaci (t)

Magani:

h = 1/2 gt ^{​​​​2}

10 = 1/2 (10) t ²

10 = 5 t ²

t ² = 10/5 = 2

t = √2 = daƙiƙa 1.4

Tazarar lokaci = daƙiƙa 1.4.

Jimlar tazara tsakanin lokaci = daƙiƙa 4 + daƙiƙa 1.4 = daƙiƙa 5.4.

[irp]

4. Ana hasashen ƙaramin ƙwallo a kwance tare da saurin farko v _o = 15 m/s daga gini mai tsayin mita 5. Lissafa lokacin da ke cikin iska ! Saurin nauyi shine 10 m/s ²

An sani:

Tsawo (h) = mita 5

Saurin farko (v _o ) = 15 m/s

Saurin nauyi (g) = 10 m/s ²

Ana so: Lokaci a sararin sama (t)

Magani:

Ana ƙididdige lokaci a cikin iska ta amfani da lissafin motsi na faɗuwa cikin 'yanci.

An sani:

Tsawo (h) = mita 5

Saurin nauyi (g) = 10 m/s ²

Ana so: Tazarar lokaci (t)

Magani:

h = 1/2 gt ^{​​​​2}

5 = 1/2 (10) t ²

5 = 5 t ²

t ² = 5/5 = 1

t = √1 = daƙiƙa 1

[irp]

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[wpdm_package id='536′]

1. Warware saurin farko zuwa sassan kwance da a tsaye
2. Ƙayyade ƙaura a kwance
3. Ƙayyade matsakaicin tsayi
4. Ƙayyade tazarar lokaci
5. Ƙayyade matsayin abubuwa
6. Ƙayyade saurin ƙarshe

Karin bayani

An warware matsalolin da ke cikin motsin harsashi - ƙayyade matsakaicin tsayi

1. Ƙwallon ƙafa da aka harba ta bar ƙasa a kusurwa θ = 60 ^o tare da kwance yana da saurin farko na 10 m/s. Lissafa matsakaicin tsayi! Saurin nauyi shine 10 m/s ².

An sani:

Kusurwoyi (θ) = 60 ^o

Saurin farko (v _o ) = 10 m/s

Ana so: Matsakaicin tsayi (h)

Magani:

Bangaren tsaye na saurin farko:

zunubi 60 ^o = v _oy / v _o

v _oy = v _o zunubi 60 ^o = (10)(zunubi 60 ^o ) = (10)(0.5 √ 3 ) = 5 √ 3 m/s

Zaɓi hanyar sama a matsayin mai kyau, kuma hanyar ƙasa a matsayin mara kyau.

An sani:

Saurin nauyi (g) = -10 m/s ² (ƙasa ta ƙasa)

Bangaren tsaye na saurin farko (v _oy ) = + 5 √ 3 m/s (mai kyau sama)

Gudu na ƙarshe a matsakaicin tsayi (v _ty ) = 0

Ana so: Matsakaicin tsayi (h)

Magani:

v _t ² = v _o ² + 2 gh

0 ² = ( 5 √ 3) ² + 2 (-10) h

0 = 2 5 ( 3) – awanni 20

0 = 75 – 20 hours

75 = awanni 20

h = 75/20

h = mita 3.75

Tsawon mafi girma shine mita 3.75.

[irp]

2. An haska jiki sama a kusurwar 30 ^o , tsayin ginin da ke kwance mita 20. Saurin farko nasa shine m4/s. A ƙididdige matsakaicin tsayin! Saurin nauyi shine m10/s ².

An sani:

Kusurwoyi (θ) = 30 ^o

Tsawon farko (h) = mita 20

Saurin farko (v _o ) = 4 m/s

Saurin nauyi (g) = 10 m/s ²

Ana so: Matsakaicin tsayi (h)

Magani:

Bangaren tsaye na saurin farko:

zunubi 30 ^o = v _oy / v _o

v _oy = v _o zunubi 30 ^o = (4)(zunubi 30 ^o ) = (4) (0.5) = 2 m/s

Zaɓi hanyar sama a matsayin mai kyau, kuma hanyar ƙasa a matsayin mara kyau.

An sani:

Saurin nauyi (g) = -10 m/s ² (ƙasa ta ƙasa)

Bangaren tsaye na saurin farko (v _oy ) = +2 m/s (mai kyau sama)

Gudu na ƙarshe a matsakaicin tsayi (v _ty ) = 0

Ana so: Matsakaicin tsayi

Magani:

Matsakaicin tsayi:

v _t ² = v _o ² + 2 gh

0 ² = 2 ² + 2 (-10) h

0 = 4 – 20 hours

4 = awanni 20

h = 4/20

h = mita 0.2

Tsawonsa mafi girma shine mita 0.2 + mita 20 = mita 20.2.

[irp]

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[wpdm_package id='536′]

1. Warware saurin farko zuwa sassan kwance da a tsaye
2. Ƙayyade ƙaura a kwance
3. Ƙayyade matsakaicin tsayi
4. Ƙayyade tazarar lokaci
5. Ƙayyade matsayin abubuwa
6. Ƙayyade saurin ƙarshe

Karin bayani

An warware matsalolin da ke cikin motsin harsashi - ƙayyade matsugunin kwance

1. Kwallon da aka harba ta bar ƙasa a kusurwa θ = 60 ^o tare da kwance yana da saurin farko na 16 m/s. Tsawon lokacin zai ɗauka kafin ƙwallon ta faɗi ƙasa?

An sani:

Kusurwoyi ( θ ) = 60 ^o

Saurin farko (v _o ) = 16 m/s

Saurin nauyi (g) = 10 m/s ²

Ana nema: Matsar da aka yi a kwance (x)

Magani:

Sashen kwance na saurin farko:

v _ox = v _o cos θ = (16 m/s) (cos 60 ^o ) = (16 m/s) (0.5) = 8 m/s

Bangaren tsaye na saurin farko:

v _oy = v _o sin θ = (16m/s)(sin 60 ^o ) = (16m/s)(0.5 √ 3 ) = 8 √ 3 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.

Lokaci a sararin samaniya

Lokacin da yake a cikin iska ana tantance shi ta hanyar motsin y. Da farko muna samun lokacin ta amfani da motsin y sannan mu yi amfani da wannan ƙimar lokaci a cikin lissafin x ( daidaitaccen lissafin gudu).

Zaɓi hanyar sama a matsayin mai kyau, kuma hanyar ƙasa a matsayin mara kyau.

An sani:

Saurin farko (v _o ) = 8 √ 3 m/s (v _o sama)

Saurin nauyi (g) = -10 m/s ² (g ƙasa)

Tsawo (h) = 0 (ƙwallon ta koma matsayi ɗaya)

Ana so: Lokaci a Iska

Magani:

h = v _o t + 1/2 gt ^{​​​​2}

0 = ( 8 √ 3) t + 1/2 (-10) t ²

0 = 8 √ 3 t – 5 t ²

8 √ 3 t = 5 t ²

8 (1.7) = 5 t

14 = 5 t

t = 14 / 5 = daƙiƙa 2.8

Matsar da aka kwance

An sani:

Gudun (v) = 8 m/s

Tazarar lokaci (t) = daƙiƙa 2.8

Ana nema: Gudun hijira

Magani:

x = vt = (8 m/s)(2.8 s) = mita 22.4

Matsakaicin tsayin jirgin ƙasa shine mita 22.4.

[irp]

2. An haska jiki sama a kusurwar 60 ^o , kuma a kwance daga gini tsayin mita 50. Saurin farko nasa shine 30 m/s. A lissafta gudun da aka yi a kwance! Saurin nauyi shine 10 m/s ².

An sani:

Kusurwoyi ( θ ) = 60 ^o

Tsawo (h) = mita 15

Saurin farko (v _o ) = 30 m/s

Saurin nauyi (g) = 10 m/s ²

Ana so : x

Magani:

Sashen kwance na saurin farko ::

v _ox = v _o cos θ = (30m/s) (cos 60 ^o ) = (30m/s) (0.5) = 15 m/s

Bangaren tsaye na saurin farko:

v _oy = v _o sin θ = (30m/s)(sin 60 ^o ) = (30m/s)(0.5 √ 3 ) = 15 √ 3 m/s

Lokaci a sararin samaniya

Da farko mun gano lokacin ta amfani da motsin y sannan muka yi amfani da wannan ƙimar lokaci a cikin lissafin x (daidaitaccen lissafin saurin gudu). Zaɓi sama a matsayin mai kyau da ƙasa kamar mara kyau.

An sani:

Saurin farko (v _o ) = 15 √ 3 m/s (sama mai kyau)

Saurin nauyi (g) = -10 m/s ² (ƙasa ta ƙasa)

Babba (h) = -50 (Ƙasa mita 50 ƙasa da wurin farko)

Ana so : t

Magani:

h = v _o t + 1/2 gt ^{​​​​2}

-50 = ( 15 √ 3 ) t + 1/2 (-10) t ²

-50 = 15 √ 3 t – 5 t ²

5 t ² – 15 √ 3 t – 50 = 0

Lissafa lokaci ta amfani da wannan dabarar:

a = 5, b = – 15 √ 3, c = – 50

Lokacin da ake buƙata shine daƙiƙa 6.7.

Matsar da aka yi a kwance:

An sani:

Gudun (v) = 15 m/s

Tazarar lokaci (t) = daƙiƙa 6.7

Ana nema: ƙaura

Magani:

s = vt = (15 m/s)(6.7 s) = mita 100.5

Matsakaicin tsayin jirgin ƙasa shine mita 100.5.

[irp]

3. Ana hango ƙaramin ƙwallo a kwance tare da saurin farko v _o = 10 m/s daga gini mai tsayin mita 10. Lissafa ƙaura a kwance ! Saurin nauyi shine 10 m/s ²

An sani:

Tsawo (h) = mita 10

Saurin farko (v _o ) = 10 m/s

Saurin nauyi (g) = 10 m/s ²

Ana so : x

Magani:

Sashen kwance na saurin farko = saurin farko = 10 m/s.

Lokaci a sararin samaniya

An ƙididdige lokacin da ake amfani da shi a iska ta amfani da lissafin motsi na faɗuwa kyauta.

An sani:

Saurin nauyi (g) = 10 m/s ²

Tsawo (h) = mita 10

Ana so : t

Magani:

h = 1/2 gt ^{​​​​2}

10 = 1/2 (10) t ²

10 = 5 t ²

t ² = 10 / 5 = 2

t = √2 = daƙiƙa 1.4

Matsar da aka kwance

Ana ƙididdige motsi a kwance ta amfani da lissafin motsi a saurin da ba ya canzawa.

An sani:

Gudun (v) = 10 m/s

Tazarar lokaci (t) = daƙiƙa 1.4

Ana so : x

Magani:

s = vt = (10 m/s)(1.4 s) = mita 14

Matsakaicin tsayin jirgin ƙasa shine mita 14.

[irp]

[wpdm_package id='526′]

[wpdm_package id='536′]

1. Warware saurin farko zuwa sassan kwance da a tsaye
2. Ƙayyade ƙaura a kwance
3. Ƙayyade matsakaicin tsayi
4. Ƙayyade tazarar lokaci
5. Ƙayyade matsayin abubuwa
6. Ƙayyade saurin ƙarshe

Karin bayani

An warware matsalolin motsi na harsashi - an warware saurin farko zuwa sassan kwance da tsaye

1. Ƙwallon ƙafa da aka harba ta bar ƙasa a kusurwa θ = 60^o da saurin mita 10/s. Lissafa abubuwan da suka fara saurin gudu!
An sani:
Kusurwoyi (θ) = 60^o
Saurin farko (v)_o) = 10 m/s
Ana so: v_ox kuma v_oy
Magani:
Warware saurin farko zuwa ɓangaren x (a kwance) da kuma ɓangaren y (a tsaye).
zunubi θ = v_oy /v_o —–> v_oy = v_o zunubi θ
cos θ = v_ox /v_o —–> v_ox = v_o kowa

x bangaren (a kwance):
v_ox = v_o cos θ = (10 m/s)(cos 60^o) = (10 m/s)(0.5) = 5 m/s

bangaren y (a tsaye):
v_oy = v_o zunubi θ = (10 m/s)(zunubi 60^o) = (10 m/s)(0.5√3) = 5√3 m/s

[irp]

2. Abu yana barin ƙasa a kusurwa θ = 30^o tare da ɓangaren y na saurin 10 m/s. Lissafa saurin farko!
An sani:
Kusurwoyi (θ) = 30^o
bangaren y (v)_oy) = 10 m/s
Ana so: Saurin farko (v)_o)
Magani:
v_oy = v_o zunubi θ
10 = (v_o) (zunubi 30^o)
10 = (v_o(0.5)
v_o = 10/0.5
v_o = 20m/s

[irp]

3. Sashen kwance na saurin farko shine m30/s kuma sashin tsaye na saurin farko shine m40/s. Lissafa saurin farko.
An sani:
Sashen kwance na saurin farko (v)_ox) = 30 m/s
Bangaren tsaye na saurin farko (v)_oy) = 40 m/s
Ana so: Saurin farko (v)_o)
Magani:
v_o² = v_ox² +v_oy² = 30² + 40² = 900 + 1600 = 2500
v_o = √2500
v_o = 50m/s

[irp]

4. Ana hango ƙaramin ƙwallo a kwance tare da saurin farko v_o = 6m/s. Lissafa x bangaren da y bangaren saurin farko.
An sani:
Saurin farko (v)_o) = 6 m/s
Ana so: vox da v_oy
Magani:
Kwallo yana motsawa a kwance don haka ɓangaren gudu a kwance (v)_ox) = saurin farko (v_o) = 6 m/s. Tsarin tsaye na saurin (v_oy) = 0 ba.

[irp]

[wpdm_package id='545′]

[wpdm_package id='536′]

1. Warware saurin farko zuwa sassan kwance da a tsaye
2. Ƙayyade ƙaura a kwance
3. Ƙayyade matsakaicin tsayi
4. Ƙayyade tazarar lokaci
5. Ƙayyade matsayin abubuwa
6. Ƙayyade saurin ƙarshe

Karin bayani