Tambayoyin Misali na Vector

Misalai 25 na Matsalolin Vector

1. Ƙarfi biyu suna tsaye a kan juna, kowannensu yana da girman N3 da N4. Girman da aka samu na ƙarfin biyu shine...
Tattaunawa
An san cewa:
F₁ = 3 N, F₂ = 4N
Tambaya: Menene sakamakon waɗannan vectors guda biyu?
Amsa:
Akwai vector guda biyu kawai kuma vector guda biyu suna tsaye a kan juna don haka maganin yana amfani da dabarar Pythagorean.
2. Idan girman vector A = raka'a 4, zai samar da kusurwar 30^o tare da axis mai kyau na x, to girman vector a cikin axis na x da y shine...
Tattaunawa
An san cewa:
A = raka'a 4, Kusurwa = 30^o
An tambaya: A_x da kuma A_y ?
Amsa:
3. Vectors guda biyu F₁ da kuma F₂ Kowannensu yana da girman N5 da N12, suna da wurin hulɗa iri ɗaya kuma suna fuskantar juna a kusurwar 60°, ƙimar da aka samu daga vectors guda biyu ita ce...
Tattaunawa
An san cewa:
F₁ = 5 N, F₂ = 12 N, kusurwa = 60^o
Tambaya: Menene sakamakon waɗannan vectors guda biyu?
Amsa:
Akwai vector guda biyu kawai kuma vector guda biyu ba su daidaita da juna ba (suna a kusurwar 60° ga juna).^o) saboda haka mafita ga matsalar tana amfani da dabarar cosine.
4. a cikin₁ = raka'a 20 da v₂ = raka'a 20. Yaya girman vector ɗin da ya haifar yake?

Tattaunawa
Lissafin vector na kayan aiki:
v_1x = v₁ kowa 30^o = (20)(½√3) = -10√3
v_1y = v₁ ba 30^o = (20)(½) = 10
v_2x = v₂ kowa 30^o = (20)(½√3) = 10√3
v_2y = v₂ ba 30^o = (20)(½) = 10

v_x = v₁x + v₂x = -10√3 + 10√3 = 0
v_y = v₁y + v₂y = 10 + 10 = 20

Bayani: v_1x alamar korau saboda alkiblar v_1x a gefen hagu, tare da axis ɗin x mara kyau. v_2x yana da kyau saboda alkiblar tana zuwa dama ko kuma a alkiblar x-axis mai kyau. v_1y kuma v_2y yana da kyau saboda alkiblarsa tana sama a alkiblar y-positive. Don gano alkiblar kowace vector na sashi da kuma ko vector na sashi yana da kyau ko mara kyau, zana vector na sashi akan axis na x da y-axis kamar yadda aka nuna a misali mai lamba 2 na tambaya.

Ana ƙididdige vector ɗin da aka samu:
Girman vector ɗin da aka samu shine raka'a 20

5. Yaro yana gudu mita 80 zuwa arewa, sannan ya juya gabas mita 80 sannan ya juya kudu mita 20. wurin ƙaura abin da yaron ya yi shi ne….

A. 60 m
B. 80 m
C. mita 100
D. 120 m
E. 180 m

Tattaunawa

Matsar da kaya zuwa wurare masu nisa

Yi amfani da tsarin Pythagorean:
Arewa maso Gabas
Amsar da ta dace ita ce C

6. Budi yana tafiya mita 6 zuwa gabas, sannan mita 6 zuwa kudu, da kuma mita 2 zuwa gabas. Motar Budi daga inda ya fara aiki ita ce...

A. 20 m
B. 14 m
C. mita 12
D. 10 m
E. 8 m

Tattaunawa

Yi amfani da tsarin Pythagorean:

alkiblar kudu maso gabas
Amsar da ta dace ita ce D.

7.

Sakamakon ƙarfin uku da ke cikin hoton da ke gefe shine…

A. 24 N
B. 16 N
C. 12 N
D. 10 N
E. 4 N

Tattaunawa
An sani :
F₁ = 20 Newton, Kusurwar tsakanin F₁ kuma axis ɗin x = 0
F₂ = 20 Newton, Kusurwar tsakanin F₂ kuma axis ɗin x = 60
F₃ = 24 Newton, Kusurwar tsakanin F₃ kuma axis ɗin x = 60
An tambaya : Sakamakon ƙarfin uku (F₁, F₂ da kuma F₃)
Jawab :

Abubuwan da ke cikin vector mai ƙarfi akan gatari x da y
F_1x = (F₁)(cos 0) = (20)(1) = 20. Mai kyau saboda yana kan hanya ɗaya da axis x tabbatacce (zuwa dama)
F_1y = (F₁)(zunubi 0) = (20)(0) = 0
F_2x = (F₂)(cos 60) = (20)(0,5) = -10. Mara kyau domin yana kan hanya ɗaya da axis x korau (a hagu)
F_2y = (F₂)(zunubi 60) = (20)(0,5√3) = 10√3. Mai kyau saboda yana kan hanya ɗaya da axis y tabbatacce (sama)
F_3x = (F₃)(cos 60) = (24)(0,5) = -12. Mara kyau domin yana kan hanya ɗaya da axis x korau (a hagu)
F_3y = (F₃)(zunubi 60) = (24)(0,5√3) = -12√3. Mara kyau domin yana kan alkibla ɗaya da axis y korau (ƙasa)
Sakamakon abubuwan da ke haifar da ƙarfin vector a kan gatari x da y
F_x = F_1x - F_2x - F_3x = 20 – 10 – 12 = -2
F_y = F_1y +F_2y - F_3y = 0 + 10√3 – 12√3 = -2√3
Sakamako na uku Adadin vector gaya
Amsar da ta dace ita ce E.

8.

Ƙarfin ƙarfin F₁, F₂, da kuma F₃ yana kan zane na Cartesian kamar yadda aka nuna a hoton:
Sakamakon vectors guda uku shine…

A. √26 N
B. √76 N
C. √84 N
D. √168 N
E. √204 N

Tattaunawa
An sani :
F₁ = 12 Newton, Kusurwar tsakanin F₁ kuma axis ɗin x = 30
F₂ = 10 Newton, Kusurwar tsakanin F₂ kuma axis ɗin x = 90
F₃ = 8 Newton, Kusurwar tsakanin F₃ kuma axis ɗin x = 30
An tambaya : Sakamakon vectors guda uku masu ƙarfi (F₁, F₂ da kuma F₃)
Jawab :
Abubuwan da ke cikin vector mai ƙarfi akan gatari x da y
F_1x = (F₁)(cos 30) = (12)(0,5√3) = 6√3. Mai kyau saboda yana kan hanya ɗaya da axis x tabbatacce (zuwa dama)
F_1y = (F₁)(zunubi 30) = (12)(0,5) = 6. Mai kyau saboda yana kan hanya ɗaya da axis y tabbatacce (sama)
F_2x = (F₂)(cos 90) = (10)(0) = 0.
F_2y = (F₂)(zunubi 90) = (10)(1) = -10. Mara kyau saboda yana kan hanya ɗaya da axis y korau (ƙasa)
F_3x = (F₃)(cos 30) = (8)(0,5√3) = -4√3. Mara kyau domin yana kan alkibla ɗaya da axis x korau (a hagu)
F_3y = (F₃)(zunubi 30) = (8)(0,5) = -4. Mara kyau saboda yana kan hanya ɗaya da axis y korau (ƙasa)
Sakamakon abubuwan da ke haifar da ƙarfin vector a kan gatari x da y
F_x = F_1x +F_2x - F_3x = 6√3 + 0 – 4√3 = 2√3
F_y = F_1y - F_2y - F_3y = 6 – 10 – 4 = -8
Sakamakon vectors uku masu ƙarfi
Amsar da ta dace ita ce B.

9. Kalli hoton da ke gefe. Girman sakamakon ƙarfin uku shine…
A. 0
B. 2√3 N
C. 4√3 N
D. 8√3 N
E. 12√3 N
Tattaunawa
An sani :
F₁ = 4 Newton, Kusurwar tsakanin F₁ kuma axis ɗin x = 30
F₂ = 6√3 Newton, Kusurwar tsakanin F₂ kuma axis ɗin x = 0
F₃ = 2 Newton, Kusurwar tsakanin F₃ kuma axis ɗin x = 90
An tambaya : Girman sakamakon ƙarfin uku (F₁, F₂ da kuma F₃)
Jawab :
Abubuwan da ke cikin vector mai ƙarfi akan gatari x da y
F_1x = (F₁)(cos 30) = (4)(0,5√3) = 2√3. Mai kyau saboda yana kan hanya ɗaya da axis x tabbatacce (zuwa dama)
F_1y = (F₁)(zunubi 30) = (4)(0,5) = 2. Mai kyau saboda yana kan hanya ɗaya da axis y tabbatacce (sama)
F_2x = (F₂)(cos 0) = (6√3)(1) = -6√3. Mara kyau saboda yana kan hanya ɗaya da axis x korau (a hagu)
F_2y = (F₂)(zunubi 0) = (6√3)(0) = 0.
F_3x = (F₃)(cos 90) = (2)(0) = 0.
F_3y = (F₃)(zunubi 90) = (2)(1) = -2. Mara kyau saboda yana kan hanya ɗaya da axis y korau (ƙasa)
Sakamakon abubuwan da ke haifar da ƙarfin vector a kan gatari x da y
F_x = F_1x - F_2x +F_3x = 2√3 – 6√3 + 0 = -4√3
F_y = F_1y +F_2y - F_3y = 2 + 0 – 2 = 0
Sakamakon vectors uku masu ƙarfi
Amsar da ta dace ita ce C.

10. Yaro yana tafiya kai tsaye mita 10 zuwa yamma, sannan ya juya kudu na tsawon mita 4, sannan ya sake juya gabas na tsawon mita 13. Matsar da yaron daga wurin da ya fara...
A. mita 4 kudu maso yamma
B. Mita 5 kudu
C. Mita 5 kudu maso gabas
D. Mita 10 gabas
E. Mita 10 kudu maso gabas

Tattaunawa

Amsar da ta dace ita ce C.

11. Sakamakon ƙarfin uku da ke cikin hoton da ke gefe shine…

A. 1,0 N
B. 1,5 N
C. 1,9 N
D. 2,0 N
E. 2,3 N
Tattaunawa
Lissafa girman kowanne vector na sassa:
F_1x = 10N
F_1y = 0
F_2x = -10 cos 60 = - (10) (0,5) = - 5 N
F_2y = 10 zunubi 60 = (10) (0,87) = 8,7 N
F_3x = -12 cos 60 = - (12) (0,5) = - 6 N
F_3y = -12 zunubi 60 = - (12) (0,87) = - 10,4 N
Ƙayyade vector ɗin da aka samu:

12. An nuna vectors guda uku masu ban sha'awa a cikin hoton. Girman kowane vector shine:
|V₁ | = raka'a 30
|V₂ | = raka'a 30
|V₃ | = raka'a 40
Girman sakamakon vectors guda uku shine...
A. Raka'a 30
B. Raka'a 40
C. Raka'a 50
D. Raka'a 90
E. Raka'a 110
Tattaunawa
An san cewa:
V₁ = 30, Kusurwar da ke tsakanin V₁ kuma axis ɗin x = 30^o
V₂ = 30, Kusurwar da ke tsakanin V₂ kuma axis ɗin x = 30^o
V₃ = 40, Kusurwar da ke tsakanin V₃ kuma axis ɗin x = 0^o
Tambaya: Sakamakon vectors guda uku (V)₁, V₂ kuma V₃)
Amsa:
Abubuwan da ke cikin vector mai ƙarfi akan gatari x da y
V_1x = (V₁(kwas 30)^o) = (30)(0,5√3) = 15√3. Mai kyau saboda yana kan alkibla ɗaya da madaidaicin x (zuwa dama)
V_1y = (V₁) (zunubi 30^o) = (30)(0,5) = 15. Mai kyau saboda yana kan alkibla ɗaya da axis mai kyau na y (sama)
V_2x = (V₂(kwas 30)^o) = (30)(0,5√3) = -15√3. Komawa saboda yana kan alkibla ɗaya da komawar x-axis mara kyau (zuwa hagu)
V_2y = (V₂) (zunubi 30^o) = (30)(0,5) = 15. Mai kyau saboda yana kan alkibla ɗaya da axis mai kyau na y (sama)
V_3x = (V₃(kwas 0)^o) = (40)(1) = 40. Mai kyau saboda yana kan hanya ɗaya da madaidaicin x (zuwa dama)
V_3y = (V₃) (zunubi 0^o) = (40)(0) = 0

13. Ƙarfi biyu (wurin hulɗa) suna tsaye a kan juna, girmansu kuma shine 12 N da 5 N. Girman sakamakon ƙarfin biyu shine…
A. 17 N
B. 15 N
C. 13 N
D. 9 N
E. 7 N
Tattaunawa
An san cewa:
Salo na 1 (F)₁) = 12 Newton
Salo na 2 (F)₂) = 5 Newton
Ana nema: Sakamakon duka ƙarfin biyu (ΣF)
Amsa:
Ƙarfin biyu suna tsaye a kan juna don haka ana ƙididdige ƙarfin da ya haifar ta amfani da dabarar Pythagorean.

14. An nuna vector guda uku masu ban sha'awa a cikin hoton da ke ƙasa. Girman kowane vector shine:
|V₁| = raka'a 30
|V₂| = raka'a 30
|V₃| = raka'a 40
Girman sakamakon vectors guda uku shine...
A. Raka'a 30
B. Raka'a 40
C. Raka'a 50
D. Raka'a 90
E. Raka'a 110
Tattaunawa
An san cewa:
v₁ = raka'a 30, suna samar da kusurwar 30^o zuwa ga axis ɗin x mara kyau.
v₂ = raka'a 30, suna samar da kusurwar 30^o zuwa ga axis ɗin x mai kyau.
v₃ = raka'a 40, suna samar da kusurwar 0^o zuwa ga axis ɗin x mai kyau.
An tambaya: Vector mai sakamako
Amsa:
Lissafa abubuwan da aka haɗa na vector:
v_1x = v₁ kowa 30^o = (30)(0,5√3) = -15√3 (alamar korau saboda tana kan alkibla ɗaya da axis ɗin x mara korau)
v_1y = v₁ ba 30^o = (30)(0,5) = 15 (alama mai kyau saboda tana kan alkibla ɗaya da axis mai kyau na y)
v_2x = v₂ kowa 30^o = (30)(0,5√3) = 15√3 (alama mai kyau saboda tana kan alkibla ɗaya da axis mai kyau na x)
v_2y = v₂ ba 30^o = (30)(0,5) = 15 (alama mai kyau saboda tana kan alkibla ɗaya da axis mai kyau na y)
v_3x = v₃ kowa 0^o = (40)(1) = 40 (alama mai kyau saboda tana kan alkibla ɗaya da axis mai kyau na x)
v_3y = v₃ ba 0^o = (40)(0) = 0

15. Sakamakon ƙarfin uku da ke cikin hoton da ke ƙasa shine...
A. 0 N
B. 2 N
C. 2√3 N
D. 3 N
E. 3√3 N
Tattaunawa
An san cewa:
F₁ = 3 Newtons suna samar da kusurwar 60^o zuwa ga axis ɗin x mai kyau
F₂ = 3 Newtons suna samar da kusurwar 0^o zuwa ga axis ɗin x mara kyau
F₃ = 6 Newtons suna samar da kusurwar 60^o zuwa ga axis na y mara kyau
An tambaya: Ƙarfin sakamako
Amsa:
Lissafa vector ɗin kayan aikin:
F_1x = F₁ kowa 60^o = (3)(0,5) = 1,5 N (alama mai kyau saboda tana kan alkiblar x-axis mai kyau)
F_1y = F₁ ba 60^o = (3)(0,5√3) = 1,5√3 N (alama mai kyau saboda tana kan alkiblar y mai kyau)
F_2x = F₂ kowa 0^o = (3)(1) = -3 N (alamar korau saboda tana kan alkiblar x-axis mara kyau)
F_2y = F₂ ba 0^o = (3)(0) = 0
F_3x = F₃ kowa 60^o = (6)(0,5) = 3 N (alama mai kyau saboda tana kan alkiblar x-axis mai kyau)
F_3y = F₃ ba 60^o = (6)(0,5√3) = -3√3 N (alamar korau saboda tana cikin alkiblar y-axis mara korau)

16. Vectors guda biyu F₁ da kuma F₂ Kowannensu yana da girman N15 da N9, suna da wurin hulɗa iri ɗaya kuma suna fuskantar juna a kusurwar 60°, ƙimar da aka samu daga vectors guda biyu ita ce...
A. 15 N
B. 20 N
C. 21 N
D. 24 N
E. 30 N
Tattaunawa
An san cewa:
Salo na 1 (F)₁) = 15 Newton
Salo na 2 (F)₂) = 9 Newton
Kusurwoyi (θ) = 60^o
Tambaya: Sakamakon vectors guda biyu
Amsa:
Akwai vector guda biyu da suka samar da kusurwar 60^o don haka ana ƙididdige vector ɗin da aka samu ta amfani da dabarar cosine:

17. Sakamakon ƙarfin uku da ke cikin hoton da ke gefe shine…
A. 24 N
B. 16 N
C. 12 N
D. 10 N
E. 4 N
Tattaunawa
An san cewa:
F₁ = 20 Newton, Kusurwar tsakanin F₁ kuma axis ɗin x = 0
F₂ = 20 Newton, Kusurwar tsakanin F₂ kuma axis ɗin x = 60
F₃ = 24 Newton, Kusurwar tsakanin F₃ kuma axis ɗin x = 60
Tambaya: Sakamakon rundunonin uku (F₁, F₂ da kuma F₃)
Amsa:
Abubuwan da ke cikin vector mai ƙarfi akan gatari x da y
F_1x = (F₁)(cos 0) = (20)(1) = 20. Mai kyau saboda yana kan hanya ɗaya da madaidaicin x (zuwa dama)
F_1y = (F₁)(zunubi 0) = (20)(0) = 0
F_2x = (F₂)(cos 60) = (20)(0,5) = -10. Komawa saboda yana kan alkibla ɗaya da komawar x-axis mara kyau (zuwa hagu)
F_2y = (F₂)(zunubi 60) = (20)(0,5√3) = 10√3. Mai kyau saboda yana kan hanya ɗaya da madaidaicin y (sama)
F_3x = (F₃)(cos 60) = (24)(0,5) = -12. Komawa saboda yana kan alkibla ɗaya da komawar x-axis mara kyau (zuwa hagu)
F_3y = (F₃)(zunubi 60) = (24)(0,5√3) = -12√3. Mara kyau domin yana kan hanya ɗaya da mara kyau ta y (ƙasa)

18. Abu yana motsawa daga E zuwa F kuma ya ƙare a G. Hoton da ke ƙasa, wanda ke nuna matsugunin raka'a 10,...

Tattaunawa

Daidaitowar maki E = x, y = 1, 1

Daidaitowar maki F = x, y = 9, 1

Daidaitowar maki G = x, y = 9, 7

Tsawon EF = 9-1 = 8

Tsawon FG = 7-1 = 6

Tsawon EG =

Amsar da ta dace ita ce A.

19. Mutum yana tafiya da mota daga A zuwa B, kilomita 30 arewa, sannan ya ci gaba zuwa C, kilomita 60 gabas, sannan daga ƙarshe ya isa birnin D, kilomita 110 kudu. Motar ta yi tafiya daga A zuwa D...

A. 200 km

B. 140 km

C. 120 km

D. 100 km

E. 80 km

Tattaunawa

AA' = 60 km

A'D = 110 km - 30 km = 80 km

Amsar da ta dace ita ce D.

20. Andi ya yi tafiya da mota daga birni A zuwa arewa zuwa birni B na tsawon kilomita 100, sannan ya ci gaba da tafiyarsa zuwa birni C gabas na tsawon kilomita 60, sannan Andi ya yi tafiya kudu zuwa birni D na tsawon kilomita 20. Motar ta…

A. 10 km

B. 20 km

C. 80 km

D. 100 km

E. 180 km

Tattaunawa

D'D = 60 km

AD' = 100 km - 20 km = 80 km

Amsar da ta dace ita ce D.

21. A taron "Bikin Marathon na Birni" a watan Oktoban 2014 a Jakarta, an sami rukunoni guda 4 na gudu, wato rukunoni cikakken marathon (kilomita 42), rukuni rabin marathon (kilomita 21), rukuni na kilomita 10 da kuma rukuni na kilomita 5, inda aka ƙayyade hanyar da kowace rukuni za ta bi. Wannan tseren marathon ya fara ne daga Bung Karno Sports Complex kuma ya ƙare a National Monument (Monas). Ɗaya daga cikin mahalarta tseren, Andri, ya shiga tseren. cikakken marathon kuma yana iya tafiya ne kawai daga wurare A, B, da C kamar haka Hoto na 2.

Idan akwati 1 yana wakiltar kilomita 1, to jimillar gudun hijirar da Andri ya yi zai kasance…

A. 26 km

B. 20 km

C. 12 km

D. 10 km

E. 8 km

Tattaunawa

Tsawon gefen ƙasa = kilomita 8, tsawon gefen gaba = kilomita 6.

Ta amfani da dabarar Pythagorean, Matsugunin = R = 10 km

Amsar da ta dace ita ce D.

22. Mutum yana tafiya da mota daga A zuwa B, kilomita 30 arewa, sannan ya ci gaba zuwa C, kilomita 60 gabas, sannan daga ƙarshe ya isa birnin D, kilomita 110 kudu. Motar ta yi tafiya daga A zuwa D...

A. 200 km

B. 140 km

C. 120 km

D. 100 km

E. 80 km

Tattaunawa

AA' = 60 km

A'D = 110 km - 30 km = 80 km

Amsar da ta dace ita ce D.

23. Andi ya yi tafiya da mota daga birni A zuwa arewa zuwa birni B na tsawon kilomita 100, sannan ya ci gaba da tafiyarsa zuwa birni C gabas na tsawon kilomita 60, sannan Andi ya yi tafiya kudu zuwa birni D na tsawon kilomita 20. Motar ta…

A. 10 km

B. 20 km

C. 80 km

D. 100 km

E. 180 km

Tattaunawa

D'D = 60 km

AD' = 100 km - 20 km = 80 km

Amsar da ta dace ita ce D.

Vektor na Naúrar

24. Tambayoyin Jarrabawar Ƙasa na 2000/2001
Abu wanda asalinsa yake a wurin tunani yana motsawa da sauri v = (2i − 1,5h) ms^-1Bayan ya yi motsi na tsawon daƙiƙa 4, abin ya motsa nesa da…
A. 2 m
B. 10 m
C. mita 12
D. 14 m
E. 25 m
Tattaunawa
An san cewa:
Gudun a cikin shugabanci na kwance (v_x) = 2 m/s
Gudun a tsaye (v_y) = 1,5 m/s
Tazarar lokaci (t) = daƙiƙa 4
An tambaya: Komawar abubuwa
Amsa:
Lissafa saurin da aka samu na abu (v):

25. Tambayoyin Jarrabawar Ƙasa na 2007/2008 P4 No. 3
Vektor F₁ = 14 N da F₂ = 10 N an sanya shi a kan zane na Cartesian kamar yadda aka nuna a cikin hoton. Vektor ɗin da aka samu idan aka bayyana a cikin vektor naúrar R = i + j shine….
A. 7i + 10√3 j
B. 7i + 10j
C. 3i + 7√3 j
D. 3i + 10j
E. 3i + 7j
Tattaunawa
Lissafin vector na kayan aiki:
F_1x = (F₁(kwas 60)^o) = (14)(0,5) = -7 N (alamar korau saboda tana cikin alkiblar x korau)
F_1y = (F₁) (zunubi 60^o) = (14)(0,5√3) = 7√3 N (alama mai kyau saboda tana kan alkiblar y mai kyau)
F_2x = 10N
F_2y = 0
Ana ƙididdige vector ɗin ɓangaren da aka samu:
F_x = F_1x +F_2x +F_3x = -7 + 10 = 3 N
F_y = F_1y +F_2y +F_3y = 7√3 + 0 = 7√3 N
Vektor ɗin da aka samu idan aka bayyana shi a cikin vektor naúrar:
R = 3 i + 7√3 j
Amsar da ta dace ita ce C.

 

Tushen tambaya:

Tambayoyin Nazarin Fizik na Ƙasa ga Makarantar Sakandare ta Babbar Sakandare/Makarantar Sakandare ta Sana'a

Tambayoyin Vector
1. Ƙarfi biyu suna tsaye a kan juna, girmansu kuma shine 5 N da 12 N. Girman sakamakon ƙarfin biyu shine ... (Amsa: 13 N)
2. Idan girman vector B = raka'a 10, zai samar da kusurwar 60^o tare da axis mai kyau na x, to girman vector a cikin axis na x da axis na y shine ... (Amsa: B_x = 5, B_y = 5√3 )
3. Vectors guda biyu F₁ da kuma F₂ Kowannensu girmansa shine 3 N da 4 N, yana da wurin hulɗa iri ɗaya kuma yana da kusurwar 60°, ƙimar da aka samu daga vectors guda biyu... (Amsa: F = √37 N)
4. a cikin₁ = raka'a 50 da v₂ = raka'a 50. Yaya girman vector ɗin da ya haifar yake?

(Amsa: v = 50√Raka'a 2)
5. Yaro yana tafiya kai tsaye mita 80 zuwa arewa, sannan ya juya gabas na mita 80, sannan ya sake juya kudu na mita 20. Matsar da yaron ya yi daga wurin da ya fara zama shine….
(Amsa: Mita 100, zuwa arewa maso gabas)
6. Sakamakon ƙarfin uku da ke cikin hoton da ke ƙasa shine...
(Amsa: 6 N)