Question

Vector A has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y-axis. What are the x and y components of vector

A. Ax = 4.29 and Ay = 2.16
B. Ax = 3.83 and Ay = -3.21
C. Ax = -3.83 and Ay = -3.21
D. Ax = -3.21 and Ay = -3.83
E. Ax = -3.21 and Ay = 3.83
F. Ax = 3.83 and Ay = 3.21

Answer 1

The x and y components of vector A are determined using cosine and sine functions with the angle from the positive x-axis. The components are Ax = -3.83 and Ay = -3.21, which corresponds to option C.

Step-by-step explanation:

To find the x and y components of vector A, we need to apply trigonometric functions, specifically cosine and sine, to decompose the vector into its perpendicular components. The angle given is 40.0° clockwise from the negative y-axis, which is equivalent to 180° + 40.0° = 220.0° counterclockwise from the positive x-axis. Since the magnitude of vector A is 5.00, we can calculate its components.

To find Ax, the x-component:
Ax = A cos θAx = 5.00 cos(220.0°)Ax = 5.00 * (-0.7660)Ax = -3.83

To find Ay, the y-component:
Ay = A sin θAy = 5.00 sin(220.0°)Ay = 5.00 * (-0.6428)Ay = -3.21

Using trigonometric functions, the x-component (Ax) is -3.83, and the y-component (Ay) is -3.21, which corresponds to answer C.