Answer:
8.57 m
Explanation:
To solve the problem, we have to decompose the two vectors along the two directions first:
Vector A:
- x component: Ax = +9.66 m
- y compoment: Ay = 0 (the vector lies along the x-axis)
Vector B:
- x component: [tex]B_x = -(12.0 m) cos 45^{\circ}=-8.49 m[/tex]
- y component: [tex]B_y = (12.0 m) sin 45^{\circ}=8.49 m[/tex]
So now we can find the sum of the two vectors by adding the components along each axis:
[tex]R_x = A_x + B_x = 9.66 m - 8.49 m = 1.17 m[/tex]
[tex]R_y = A_y + B_y = 0 + 8.49 m = 8.49 m[/tex]
And the magnitude of the sum is given by Pythagorean theorem:
[tex]R=\sqrt{R_x^2+R_y^2}=\sqrt{(1.17 m)^2+(8.49 m)^2}=8.57 m[/tex]
