Question

selasieKOPsBunPANTOPERE. O 11.18 m, 148.435 deg14. Given the vectors A = 50 m 10 degnorth of east and B = 100 m 80 deg south of west,find the x and y components of their sum vector A + B. (1 point)A. O(31.876 m, -89.798 m)B. (18.694 m, -130.237 m)C. O(6.913 m. -76.906 m)D. O(6.913 m, -89.798 m)E. O(31.876 m. -76.906 m)70.50

Answer 1

Given:

The vector A is 50 m 10 deg north of east.

The vector B is 100 m 80 deg south of west.

To find the x and y components of their sum vector A+B

Explanation:

The vectors can be represented in diagram as shown below

The x-component can be calculated as

$\begin{gathered} A_x+B_x=\text{ 50 cos \lparen10}^{\circ}\text{\rparen-100 cos\lparen80}^{\circ}\text{\rparen} \\ =\text{ 31.876 m} \end{gathered}$

The y-component can be calculated as

$\begin{gathered} A_y+B_y=50sin(10^{\circ})-100sin(80^{\circ}) \\ =-89.798 \end{gathered}$

Thus, option A is correct.