Chapter 2, Problem 2.8CYU

Check Your understanding Three displacement vectors $\stackrel{\to }{\text{A}}$ , $\stackrel{\to }{\text{B}}$ , and $\stackrel{\to }{\text{F}}$ in (Figure 2.13) are specified by their magnitudes $A=10.0,B=7.0$ and $F=20.00$ , respectively, and by their respective direction angles with the horizontal direction $\alpha =35°,\beta =-110°$ , and $\phi =110°$ . The physical units of the magnitudes are centimeters. Use the analytical method to find vector $\stackrel{\to }{\text{G}}=\stackrel{\to }{\text{A}}+2\stackrel{\to }{\text{B}}-\stackrel{\to }{\text{F}}$ . Verify that $G=28.1\text{5 cm}$ and that ${\theta }_G=-68.65°$ .

The three displacement vectors $\stackrel{\to }{\text{A}}$ , $\stackrel{\to }{\text{B}}$ , and $\stackrel{\to }{\text{C}}$ in Figure are specified by their magnitudes $A=10.0,B=7.0$ and $C=8.0$ , respectively, and by their respective direction angles with the horizontal direction $\alpha =35°,\beta =110°$ , and $\gamma =30°$ . The physical units of the magnitudes are centimeters. Choose a convenient scale and use a ruler and a protractor to find the following vector sums: (a) $\stackrel{\to }{\text{R}}=\stackrel{\to }{\text{A}}+\stackrel{\to }{\text{B}}$ , (b) $\stackrel{\to }{\text{D}}=\stackrel{\to }{\text{A}}-\stackrel{\to }{\text{B}}$ , and (c) $\stackrel{\to }{\text{S}}=\stackrel{\to }{\text{A}}-3\stackrel{\to }{\text{B}}+\stackrel{\to }{\text{C}}$ .