Question

B. O 1.3 cm, 90 degC. O 1.3 cm, -90 degD. O2.6 cm, 90 degE. O2.6 cm, -90 deg7. Given the vectors A = 4 m east and B = 3 m south, using graphicaladdition determine which of the following most likely representthe magnitude and direction of the sum vector (A + B) respectively.(You should be able to answer it with sketches not drawn to scale.) (1 pointA. O5 m, 323.13 degB. 07 m, 323.13 degC. O5 m, 216.87 degD. O 5 m, 36.87 degE. 07 m, 216.87 deg

Answer 1

Given:

The vector A is,

$\vec{A}=4\text{ m east}$

The vector B is,

$\vec{B}=3\text{ m south}$

To find:

the addition using the graphical method

Explanation:

The graphical representation is shown below:

The magnitude of the vector sum of the given vectors is,

$\begin{gathered} \vec{A}+\vec{B}=\sqrt{A^2+B^2} \\ =\sqrt{4^2+3^2} \\ =\sqrt{16+9} \\ =\sqrt{25} \\ =5\text{ m} \end{gathered}$

The angle with the east is,

$\begin{gathered} \theta=tan^{-1}\frac{B}{A} \\ =tan^{-1}\frac{3}{4} \\ =36.87\degree \end{gathered}$

Hence, the sum of the vectors is,

$5\text{ m, 36.87}\degree$