Yaadannoo boqonnaa fi gaaffii shaakalaa

Boqonnaa 2 Fiizikii kutaa 11: Vectors

Wanti fuula kana irra jiru hundi boqonnaa 2 kitaaba Fiizikii kutaa 11 tiif: wanta boqonnaan haguugu, yaadannoo gabaabaa, gaaffii shaakalaa deebii isaanii waliin, fi viidiyoo barnootaa bakka jirutti.

5
Kaardii: 10
Gaaffii shaakalaa boqonnaa 2: 17–46
Fuula kitaabaa boqonnaa 2

Yaadannoo gabaabaa boqonnaa 2

Kaardiiwwan fuula Fiizikii kutaa 11 irratti boqonnaa kana jala galmaa'an. Tokko tokkoon bani.

Tan^-1 yeroo fayyadamtan kallattii sirrii filadhuDogoggora baratame

Yoom akka itti fayyadamtu

Kallattii bu'aa tan^-1 R_y/R_x irraa yoo argattan, kaa'iinsa x-axis irraa yoo ibsitan fayyadami.

Of eeggadhu

Calculator tan^-1 kaa'iinsa -90 hanga 90 digirii qofa kenna. Mallattoo R_x fi R_y xy-axis irratti mirkaneessi, kaa'iinsa ceyyii sirrii keessatti kaa. Fakkeenyaaf R_x mallattoo hir'ate, R_y mallattoo qabeessa yoo ta'e, kaa'iinsi x-axis hir'ate irra ol ta'a.

Grade 11 Physics, fuula 17-46 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Qindaa'ina vektaraFoormulaa

A_x=A\cos\theta \qquad A_y=A\sin\theta

A_x=A\cos\theta \qquad A_y=A\sin\theta

$A$: Guddina vektara $same as the vector, e.g. m or N$
$\theta$: Kaa'iinsa x-axis irraa tilmaamame $\degree$
$A_x$: Qindaa'ina x ti A $same as the vector, e.g. m or N$
$A_y$: Qindaa'ina y ti A $same as the vector, e.g. m or N$

Yoom akka itti fayyadamtu

Vektara gara qindaa'ina x fi y isaa yoo qoodan, kaa'iinsi irra deebiin x-axis irraa yoo tilmaamame fayyadami.

Of eeggadhu

Kaa'iinsi y-axis irraa yoo tilmaamame cos qindaa'ina y wajjin, sin qindaa'ina x wajjin ni ta'a. Axis sirrii ta'e mirkaneeffadhu.

Grade 11 Physics, fuula 17-46 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Guddina bu'aa qindaa'ina isaa irraaFoormulaa

R=\sqrt{R_x^{2}+R_y^{2}}

R=\sqrt{R_x^{2}+R_y^{2}}

$R$: Guddina vektara bu'aa (resultant) $same as the vectors, e.g. m or N$
$R_x$: Qindaa'ina x resultant; walitti makamuu qindaa'ina x vektaroota $same as the vectors, e.g. m or N$
$R_y$: Qindaa'ina y resultant; walitti makamuu qindaa'ina y vektaroota $same as the vectors, e.g. m or N$

Yoom akka itti fayyadamtu

Vektaroota component method fayyadamuun yoo walitti darbitan, guddina vektara bu'aa barbaaddan fayyadami.

Grade 11 Physics, fuula 17-46 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Guddina walitti makamuu guddina hin ta'uDogoggora baratame

Yoom akka itti fayyadamtu

Vektarota kallattii walfakkaatu hin qabne lamaa yoo walitti darbitan, guddina bu'aa barbaaddan fayyadami.

Of eeggadhu

|A+B| = |A|+|B| yeroo vektarotni walqixa ta'an qofa. Humna 3 N fi 4 N kallattii gaaffii sadarkaa 90 ta'e irraa bu'aan 5 N dha, 7 N miti.

Grade 11 Physics, fuula 17-46 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Oomisha qabaa (dot product) vektaroota lamaaFoormulaa

\vec{A}\cdot\vec{B}=AB\cos\theta=A_xB_x+A_yB_y

\vec{A}\cdot\vec{B}=AB\cos\theta=A_xB_x+A_yB_y

$A$: Guddina vektara A $same as the vector A, e.g. N or m$
$B$: Guddina vektara B $same as the vector B, e.g. N or m$
$\theta$: Kaa'iinsa A fi B gidduu yoo mucaa mucaatti kaa'aman $\degree$

Yoom akka itti fayyadamtu

Kaa'iinsa vektaroota lamaa gidduu barbaaddu yookaan humna fi nagaaf sochii irraa hojii (work) ykn humna (power) yoo baay'isan fayyadami.

Of eeggadhu

Oomishni qabaa scalar dha, vektara miti, kanaaf kaa'iinsa hin qabu. Kaa'iinsa dubbisuu dura vektarota mucaa mucaatti kaa'i.

Grade 11 Physics, fuula 17-46 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Gaaffii shaakalaa boqonnaa 2

Gaaffii filannoo 10 boqonnaa kana irratti barreeffaman, tokkoon tokkoon isaanii deebii fi sababa qabu. Deebii banuu dura yaali. Gaaffiin kun Ingiliffaa tiin.

Gaaffii 1

Which of the following physical quantities is a vector quantity?

A.Velocity
B.Speed
C.Volume
D.Power

Deebii fi sababa agarsiisi

Deebii: A Velocity

Sababa

A vector quantity has both magnitude and direction. Velocity has both magnitude and direction, while speed, volume, and power are scalar quantities described by magnitude alone.

Gaaffii 2

If a displacement vector is 60 km toward North, what is its negative vector?

A.60 km toward South
B.60 km toward North
C.60 km toward East
D.60 km toward West

Deebii fi sababa agarsiisi

Deebii: A 60 km toward South

Sababa

The negative of a vector has the exact same magnitude as the original vector but points in the opposite direction. Opposite to North is South.

Gaaffii 3

A boat sails downstream in the Baro River. The boat moves at 0.50 m/s in still water, and the river flows in the same direction at 0.30 m/s. What is the resultant velocity of the boat?

A.0.80 m/s, downstream
B.0.20 m/s, downstream
C.0.50 m/s, upstream
D.0.15 m/s, downstream

Deebii fi sababa agarsiisi

Deebii: A 0.80 m/s, downstream

Sababa

When two collinear vectors point in the same direction, their magnitudes add directly: R = 0.50 m/s + 0.30 m/s = 0.80 m/s, downstream.

Gaaffii 4

What is the scalar (dot) product of any unit vector with itself, such as i · i?

A.1
B.0
C.-1
D.2

Deebii fi sababa agarsiisi

Deebii: A 1

Sababa

The dot product of a unit vector with itself is unity (1) because both vectors have a magnitude of 1 and the angle between them is 0 degrees (cos 0° = 1).

Gaaffii 5

According to the triangle law of vector addition, how must two vectors be connected to find their resultant?

A.Head to tail
B.Tail to tail
C.Head to head
D.Parallel without touching

Deebii fi sababa agarsiisi

Deebii: A Head to tail

Sababa

In the triangle law of vector addition, vectors are placed head to tail, and the resultant vector is drawn from the tail of the first vector to the head of the second.

Gaaffii 6

An ant walks 40 cm due South and then 50 cm due West. What is the magnitude of the ant's resultant displacement from its starting point?

A.64 cm
B.90 cm
C.10 cm
D.50 cm

Deebii fi sababa agarsiisi

Deebii: A 64 cm

Sababa

Because the two displacements are perpendicular, use the Pythagorean theorem: S = √(40² + 50²) = √(1600 + 2500) = √4100 ≈ 64 cm.

Gaaffii 7

A pushing force of magnitude 35 N acts at an angle of 40° above the negative x-axis. If cos 40° = 0.766, what is the magnitude of the x-component of this force?

A.26.8 N
B.22.5 N
C.35.0 N
D.17.5 N

Deebii fi sababa agarsiisi

Deebii: A 26.8 N

Sababa

The x-component is given by F_x = F cos 40° = 35 N × 0.766 = 26.8 N.

Gaaffii 8

A force F = (5i + 3j) N moves a block along a displacement S = (-2i + 4j) m in Hawassa. What is the work done by the force?

A.2 J
B.-2 J
C.22 J
D.14 J

Deebii fi sababa agarsiisi

Deebii: A 2 J

Sababa

Work is the dot product of force and displacement: W = F · S = (5)(-2) + (3)(4) = -10 + 12 = 2 J.

Gaaffii 9

Given the force vector F = (12i - 16j) N, what is the unit vector in the direction of F?

A.0.6i - 0.8j
B.0.8i - 0.6j
C.12i - 16j
D.0.6i + 0.8j

Deebii fi sababa agarsiisi

Deebii: A 0.6i - 0.8j

Sababa

The magnitude of F is √(12² + (-16)²) = √(144 + 256) = √400 = 20. The unit vector is (12/20)i - (16/20)j = 0.6i - 0.8j.

Gaaffii 10

An unknown vector D is added to C = (-4i + 5j) units so that the resultant R = C + D is (-i + j) units. What is vector D?

A.(3i - 4j) units
B.(-5i + 6j) units
C.(-3i + 4j) units
D.(5i - 4j) units

Deebii fi sababa agarsiisi

Deebii: A (3i - 4j) units

Sababa

For components: R_x = C_x + D_x → -1 = -4 + D_x → D_x = 3, and R_y = C_y + D_y → 1 = 5 + D_y → D_y = -4. Therefore, D = (3i - 4j) units.

Appiin boqonnaa kana irratti gaaffii 12 qaba; utuu hojjettuu ni sirreessa. Kan asii jiran 10 jalqabaa ti.

Fuula kitaabaa boqonnaa 2

Boqonnaan 2 Maxxansa Ministeera Barnootaa keessatti fuula 17 hanga fuula 46 ti.

Maxxansa Ministeera Barnootaa, Ingiliffaa, Fuula 338

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Yaadannoo gabaabaa Fiizikii kutaa 11 hunda

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