Question

Find the magnitude of the sum

Answer 1

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: $B_x = -(12.0 m) cos 45^{\circ}=-8.49 m$

- y component: $B_y = (12.0 m) sin 45^{\circ}=8.49 m$

So now we can find the sum of the two vectors by adding the components along each axis:

$R_x = A_x + B_x = 9.66 m - 8.49 m = 1.17 m$

$R_y = A_y + B_y = 0 + 8.49 m = 8.49 m$

And the magnitude of the sum is given by Pythagorean theorem:

$R=\sqrt{R_x^2+R_y^2}=\sqrt{(1.17 m)^2+(8.49 m)^2}=8.57 m$