Vector $\overrightarrow { \mathbf { M } }$ = 4.00 m points eastward and vector $\vec { N }$ = 3.00 m points southward. The resultant vector $\overrightarrow { \mathbf { M } }$ + $\vec { N }$ is given by
A) 5.00 m at an angle of 36.9° south of east.
B) 5.00 m at an angle of 53.1° south of east.
C) 5.00 m at an angle of 71.6° south of east.
D) 5.00 m at an angle of 18.4° south of east.
E) 5.00 m at an angle of 26.6° south of east.

Question

Quizplus · Accepted Answer

The resultant vector is given by the Pythagorean theorem:$$\overrightarrow { \mathbf { M } }\) + $\vec { N }$ = \sqrt{(\overrightarrow { \mathbf { M } })^2 + (\vec { N })^2} = \sqrt{(4.00 m)^2 + (3.00 m)^2} = 5.00 m$$The angle of the resultant vector is given by:$$\theta = \tan^{-1}(\frac{\vec { N }}{\overrightarrow { \mathbf { M } }}) = \tan^{-1}(\frac{3.00 m}{4.00 m}) = 36.9°$$Therefore, the resultant vector is 5.00 m at an angle of 36.9° south of east.

Vector M→\overrightarrow { \mathbf { M } }M = 400 M Points Eastward and Vector

Vector $\overrightarrow { \mathbf { M } }$ = 400 M Points Eastward and Vector