The magnitude of $\vec { A }$ is 5.5 m,and this vector lies in the second quadrant and makes an angle of 34 ° with the +y-axis.The components of $\vec { A }$ are closest to:
A) $A _ { \mathcal { X } }$ = -3.1 m, $A _ { y }$ = 4.6 m.
B) $A _ { \mathcal { X } }$ = 3.1 m, $A _ { y }$ = -4.6 m.
C) $A _ { \mathcal { X } }$ = 4.6 m, $A _ { y }$ = -3.1 m.
D) $A _ { \mathcal { X } }$ = -4.6 m, $A _ { y }$ = 3.1 m.
E) $A _ { \mathcal { X } }$ = -4.6 m, $A _ { y }$ = -3.1 m.

Question

Quizplus · Accepted Answer

Since the vector lies in the second quadrant, its x-component should be negative and its y-component should be positive. Using trigonometry, $A_x = A\cos(\theta)$ and $A_y = A\sin(\theta)$, where $\theta$ is the angle with the +y-axis, $A = 5.5$, and $\theta = 34^\circ$. Calculating gives $A_x \approx -3.1$ m and $A_y \approx 4.6$ m, matching option A.

The Magnitude Of A⃗\vec { A }A Is 55 M,and This Vector Lies in the Second Quadrant and This

The Magnitude Of $\vec { A }$ Is 55 M,and This Vector Lies in the Second Quadrant and This