18.2: Vectors

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Angalia Uelewa Wako

2.1. a. si sawa kwa sababu wao ni orthogonal; b. si sawa kwa sababu wana ukubwa tofauti; c. si sawa kwa sababu wana ukubwa tofauti na maelekezo; d. si sawa kwa sababu wao ni antiparallel; e. sawa.

2.2. 16 m;\(\vec{D}\) = -16 m\(\hat{u}\)

2.3. G = 28.2 cm,\(\theta_{G}\) = 291°

2.4. \(\vec{D}\)= (-5.0\(\hat{i}\) - 3.0\(\hat{j}\)) cm; kuruka ilihamia 5.0 cm upande wa kushoto na 3.0 cm chini kutoka kwenye tovuti yake ya kutua.

2.5. 5.83 sentimita, 211°

2.6. \(\vec{D}\)= (-20 m)\(\hat{j}\)

2.7. 35.1 m/s = 126.4 km/h

2.8. \(\vec{G}\)= (10.25 ÷\(\hat{i}\) 26.22\(\hat{j}\)) sentimita

2.9. D = 55.7 N; mwelekeo 65.7° kaskazini mwa mashariki

2.10. \(\hat{v}\)= 0.8\(\hat{i}\) + 0.6\(\hat{j}\), 36.87° kaskazini mwa mashariki

2.11. \(\vec{A} \cdotp \vec{B}\)= -57.3,\(\vec{F} \cdotp \vec{C}\) = 27.8

2.13. 131.9°

2.14. W ₁ = 1.5 J, W ₂ = 0.3 J

2.15. \(\vec{A} \times \vec{B}\)= -40.1\(\hat{k}\) au, sawa,\(\vec{A} \times \vec{B}\) | = 40.1, na mwelekeo ni ndani ya ukurasa;\(\vec{C} \times \vec{F}\) = + 157.6\(\hat{k}\) au, sawa, |\(\vec{C} \times \vec{F}\) | = 157.6, na mwelekeo hauko nje ya ukurasa.

2.16. a. -2\(\hat{k}\), b. 2, c. 153.4°, d. 135°

Maswali ya dhana

1. Scalar

3. Majibu inaweza kutofautiana

5. Sambamba, jumla ya ukubwa, antiparallel, sifuri

7. Ndiyo, ndiyo

9. Zero, ndiyo

11. Hapana

13. Sawa, sawa, sawa

15. Vector kitengo cha x-axis

17. Wao ni sawa.

19. Ndiyo

21. a. C =\(\vec{A} \cdotp \vec{B}\), b.\(\vec{C} = \vec{A} \times \vec{B}\) au\(\vec{C} = \vec{A} - \vec{B}\), c.\(\vec{C} = \vec{A} \times\vec{B}\), d.\(\vec{C}\) = A\(\vec{B}\), e., f.\(\vec{C} + 2 \vec{A} = \vec{B}\)\(\vec{C} = \vec{A} \times \vec{B}\), g. upande wa kushoto ni scalar na upande wa kulia ni vector, h.\(\vec{C} = 2 \vec{A} \times \vec{B}\), i.\(\vec{C} = \frac{\vec{A}}{B}\), j.\(\vec{C} = \frac{\vec{A}}{B}\)

23. Wao ni orthogonal.

Matatizo

25. \(\vec{h}\)= -16.4 m\(\hat{u}\), 16.4 m

27. 30.8 m, 35.7° magharibi ya kaskazini

29. 134 km, 80°

31. 7.34 km, 63.5° kusini mwa mashariki

33. 3.8 km mashariki, 3.2 km kaskazini, 7.0 km

35. 14.3 km, 65°

37. a.\(\vec{A}\) = + 8.66\(\hat{i}\) + 5.00\(\hat{j}\)

b.\(\vec{B}\) = + 3.01\(\hat{i}\) + 3.99\(\hat{j}\)

c.\(\vec{C}\) = + 6.00\(\hat{i}\) - 10.39\(\hat{j}\)

d.\(\vec{D}\) = -15.97\(\hat{i}\) + 12.04\(\hat{j}\)

f.\(\vec{F}\) = -17.32\(\hat{i}\) - 10.00\(\hat{j}\)

39. a. 1.94 km, 7.24 km

b. ushahidi

41. 3.8 km mashariki, 3.2 km kaskazini, 2.0 km,\(\vec{D}\) = (3.8\(\hat{i}\) + 3.2\(\hat{j}\)) km

43. P ₁ (2.165 m, 1.250 m), P ₂ (-1.900 m, 3.290 m), 5.27 m

45. 8.60 m, A (2\(\sqrt{5}\) m, 0.647\(\pi\)), B (3\(\sqrt{2}\) m, 0.75\(\pi\))

47. a.\(\vec{A} + \vec{B}\) = -4\(\hat{i}\) - 6\(\hat{j}\), |\(\vec{A} + \vec{B}\) | = 7.211,\(\theta\) = 236.3°

b.\(\vec{A} -\vec{B}\) = -2\(\hat{i}\) + 2\(\hat{j}\), |\(\vec{A} - \vec{B}\) | = 2\(\sqrt{2}\),\(\theta\) = 135°

49. a.\(\vec{C}\) = (\(\hat{i}\)5.0 -\(\hat{j}\) 1.0 - 3.0\(\hat{k}\)) m, C = 5.92 m

b.\(\vec{D}\) = (4.0\(\hat{i}\) - 11.0\(\hat{j}\) + 15.0\(\hat{k}\)) m, D = 19.03 m

51. \(\vec{D}\)= (3.3\(\hat{i}\) -6.6\(\hat{j}\)) km,\(\hat{i}\) ni upande wa mashariki, kilomita 7.34, -63.5°

53. a.\(\vec{R}\) = -1.35\(\hat{i}\) - 22.04\(\hat{j}\)

b.\(\vec{R}\) = -17.98\(\hat{i}\) + 0.89\(\hat{j}\)

55. \(\vec{D}\)= (200\(\hat{i}\) + 300\(\hat{j}\)) yd, D = 360.5 yd, 56.3° kaskazini mwa mashariki; Majibu ya namba yangebaki sawa lakini kitengo cha kimwili kitakuwa mita. Maana ya kimwili na umbali itakuwa sawa kwa sababu 1 yd inalinganishwa na m 1.

57. \(\vec{R}\)= —3\(\hat{i}\) - 16\(\hat{j}\)

59. \(\vec{E}\)= E\(\hat{E}\), E _x = + 178.9 V/m, E _y = -357.8 V/m, E _z = 0.0 V/m,\(\theta_{E}\) = ^{-tan -1} (2)

61. a.\(\vec{R}_{B}\) = (12.278\(\hat{i}\) + 7.089\(\hat{j}\) + 2.500\(\hat{k}\)) km,\(\vec{R}_{D}\) = (-0.262\(\hat{i}\) + 3.000\(\hat{k}\)) km

b. |\(\vec{R}_{B} − \vec{R}_{D}\) | = 14.414 km

63. a. 8.66

b. 10.39

c. 0.866

d. 17.32

65. \(\theta_{i}\)= 64.12°,\(\theta_{j}\) = 150.79°,\(\theta_{k}\) = 77.39°

67. a. -119.98\(\hat{k}\)

b. 0\(\hat{k}\)

c. +93.69\(\hat{k}\)

d. -240.0\(\hat{k}\)

e. +3.993\(\hat{k}\)

f. -3.009\(\hat{k}\)

g. +14.99\(\hat{k}\)

h. 0

69. a. 0

b. 173,194

c. +199,993\(\hat{k}\)

Matatizo ya ziada

71. a. 18.4 km na 26.2 km

b. 31.5 km na kilomita 5.56

73. a. (r,\(\phi + \frac{\pi}{2}\))

b. (2r,\(\phi + 2 \pi\))

c. (3r, -\(\phi\))

75. d _PM = 33.12 nmi = 61.34 km, d _NP = 35.47 nmi = 65.69 km

77. ushahidi

79. a. 10.00 m

b. 5\(\pi\) m, c. 0

81. 22.2 km/h, 35.8° kusini mwa magharibi

83. 240.2 m, 2.2° kusini ya magharibi

85. \(\vec{B}\)= -4.0\(\hat{i}\) + 3.0\(\hat{j}\) au\(\vec{B}\) = 4.0\(\hat{i}\) - 3.0\(\hat{j}\)

87. ushahidi

Changamoto Matatizo

89. G _\(\perp\)= 2375\(\sqrt{17}\) ≈ 9792

91. ushahidi

Wachangiaji na Majina

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