Ƙayyade tazarar lokaci na motsi mai ƙarfi

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

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.

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.

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

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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