Chapter 1: Exercises (1.41 - 1.45)

1.41 A disoriented physics professor drives 325 km north, then 4.75 km west, and then 1.50 km south. Find the magnitude and direction of the resultant displacement, using the method of components.

1.42 Vector $\vec{A}$ has components $A_{x} = 1.30 cm, A_{y} = 2.25 cm$; vector $\vec{B}$ has components $B_{x} = 4.10 cm, B_{y} = -3.75 cm$. Find a) the components of the vector sum $\vec{A} + \vec{B}$; b) the magnitude and direction of $\vec{A} + \vec{B}$; c) the components of the vector difference $\vec{B} - \vec{A}$; b) the magnitude and direction of $\vec{B} - \vec{A}$;

1.43 Vector $\vec{A}$ is 2.80 cm long and is $60.0^{\circ}$ above the x-axis in the first quadrant. Vector $\vec{B}$ is 1.90 cm long and is $60.0^{\circ}$ below the x-axis in the fourth quadrant (Fig. 1.29). Find the magnitude and direction of a) $\vec{A} + \vec{B}$; b) $\vec{A} - \vec{B}$; c) $\vec{B} - \vec{A}$. In each case, sketch the vector addition or subtraction and show that your numerical answers are in qualitative agreement with your sketch.

Section 1.9 Unit Vectors

1.44 Write each vector in Fig. 1.27 in terms of the unit vectors $\hat{i}$ and $\hat{j}$.

1.45 Write each vector in Fig. 1.28 in terms of the unit vectors $\hat{i}$ and $\hat{j}$.