Vector $\vec { A }$ has a magnitude of 7.0 m and points 30° east of north. Vector $\overrightarrow { \mathbf { B } }$ has a magnitude of 5.0 m and points 30° west of south. The resultant vector $\vec { A }$ + $\overrightarrow { \mathbf { B } }$ is given by
A) 10.0 m at an angle 60° north of east.
B) 10.0 m at an angle 30° east of north.
C) 2.0 m at an angle 30° north of east.
D) 2.0 m at an angle 60° north of east.
E) 1.0 m at an angle 60° east of north

Question

Quizplus · Accepted Answer

The vectors $\vec{A}$ and $\vec{B}$ can be broken into components. $\vec{A}$ has components $A_x = 7 \sin(30^\circ)$ and $A_y = 7 \cos(30^\circ)$. $\vec{B}$ has components $B_x = -5 \sin(30^\circ)$ and $B_y = -5 \cos(30^\circ)$. Adding these gives resultant components $R_x = 7 \sin(30^\circ) - 5 \sin(30^\circ)$ and $R_y = 7 \cos(30^\circ) - 5 \cos(30^\circ)$. Calculating these gives $R_x = 1$ and $R_y = 2$, resulting in a magnitude of $\sqrt{1^2 + 2^2} = \sqrt{5} \approx 2.24$ m, and an angle $\tan^{-1}(2/1) = 63.4^\circ$, approximately 60° north of east.

Vector A⃗\vec { A }A Has a Magnitude of 7 B→\overrightarrow { \mathbf { B } }B

Vector $\vec { A }$ Has a Magnitude of 7 $\overrightarrow { \mathbf { B } }$