1. c. The graphical construction of $\vec{A}{}_1+\vec{A}{}_2+\vec{A}{}_3$ is shown in the figure.

2. b. The graphical construction of $2\vec{A}-\vec{B}$ is shown in the figure.

3. $\mathit{C}\mathit{x}\mathbf{=}\mathbf{-}\mathbf{4}\mathbf{\text{cm}}\mathbf{\text{,}}\mathit{C}\mathit{y}\mathbf{=}\mathbf{2}\mathbf{\text{cm}}$

4. c. Vector $\vec{C}$ points to the left and down, so both $C_x$ and $C_y$ are negative. $C_x$ is in the numerator because it is the side opposite $\varphi$.

1.

• a.

  

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• b.

  

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3.

1. $E\text{sin}\theta \text{,}-E\text{cos}\theta$

2. $E\text{cos}\varphi \text{,}-E\text{sin}\varphi$

5. 8 m

7.

1. 3.8 m/s, 6.5 m/s

2. $1.3\text{m}\text{/}{\text{s}}^2\text{,}0.80\text{m}\text{/}{\text{s}}^2$

3. $-30\text{N,}40\text{N}$

9. 100 m, west

11.

1. $5.7\text{,}45\text{°}$

2. $2.2\text{cm,}27\text{°}$

3. $100\text{m/s,}84\text{°}$

4. $22{\text{m/s}}^2\text{,}27\text{°}$

13.

• a. $4î-ĵ$

• b.

  

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• c. $14\text{°}\text{below the }+x\text{-}\text{axis}$

15.

• a. $7î-7ĵ$

• b.

  

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• c. $9.9\text{,}45\text{°}$

17.

1. 2.8

2. 4.1

3. 6.1

19. $-0.071î+4.6ĵ$

21. $B_x=-2.5\text{m, }B{}_y=4.3\text{m; }B{}_x=0.0\text{m, }B{}_y=5.0\text{m}$

23.

1. 0 m, 26, 160 m

2. $\vec{v}\left(t\right)=(10î+8.0ĵ)t\text{m}\text{/}\text{s}$

3. 0 m/s, 26 m/s, 6 m/s

25. $\vec{C}=0.8î-4.5ĵ$

27. $\vec{B}={\displaystyle \frac{1}{\sqrt{2}}}î+{\displaystyle \frac{1}{\sqrt{2}}}ĵ$

29.

1. 100 m lower

2. 5.0 km

31. 90 m, $46\text{°}$ south of west

33. $31\text{°}$

35.

1. $34\text{°}$

2. 1.7 m/s

37.

1. $-3.4\text{m}\text{/}\text{s}$

2. $-9.4\text{m}\text{/}\text{s}$

39. $T_x=450\text{N, }{T}_y=310\text{N}$

41. $25\text{°}$ west of north, 385 paces

43. 4.4 units at $83\text{°}$ below the negative x-axis

45.

1. $(2.9\text{N})ĵ$

2. $(-1.6\text{N})î$