Chapter 1: Exercises (1.36 - 1.40)

1.36 Let the angle $\theta$ be the angle that the vector $\overrightarrow{A}$ makes with the +x-axis, measured counterclockwise from that axis. Find the angle $\theta$ for a vector that has the following components: a) $A_{x}$ = 2.00 m, $A_{y}$ = -1.00 m; b) $A_{x}$ = 2.00 m, $A_{y}$ = 1.00 m; c) $A_{x}$ = -2.00 m, $A_{y}$ = 1.00 m; d) $A_{x}$ = -2.00 m, $A_{y}$ = -1.00 m.

1.37 A rocket fires two engines simultaneously. One produces a thrust of 735 N directly forward while the other gives a 513 N thrust at $32.4^{\circ}$ above the forward direction. Find the magnitude and direction (relative to the forward direction) of the resultant force which these engines exert on the rocket.

1.38 A postal employee drives a delivery truck over the route shown in Fig. 1.26. Use the method of components to determine the magnitude and direction of her resultant displacement. In a vector addition diagram (roughly to scale), show that the resultant displacement found from your diagram is in qualitative agreement with the result you obtained using the method of components.

1.39 For the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ in Fig. 1.27, use the method of components to find the magnitude and direction of a) the vector sum $\overrightarrow{A} + \overrightarrow{B}$; b) the vector sum $\overrightarrow{B} + \overrightarrow{A}$; c) the vector difference $\overrightarrow{A} - \overrightarrow{B}$; d) the vector difference $\overrightarrow{B} - \overrightarrow{A}$.

1.40 Find the magnitude and direction of the vector represented by the following pair of components: a) $A_{x}$ = -8.60 cm, $A_{y}$ = 5.20 cm; b) $A_{x}$ = -9.70 m, $A_{y}$ = 2.45 m; c) $A_{x}$ = 7.75 km, $A_{y}$ = 2.70 km.