Final answer:
The magnitude of vx is approximately 3.46 meters/second, which is found by multiplying the velocity by the cosine of 30°.
Step-by-step explanation:
The question asks to find the magnitude of vx, which is the x-component of the velocity vector v, given that v has a magnitude of 4.00 meters/second and makes an angle of 60° with the positive direction of the y-axis. The x-component of the velocity is found by using the formula vx = v × cos(θ), where θ is the angle the velocity makes with the x-axis. Since the angle given is with the y-axis, we need to use its complement with the x-axis, which is 30° (90° - 60°). Therefore, vx = 4.00 m/s × cos(30°) = 4.00 m/s × √3/2 ≈ 3.46 m/s.