Final answer:
The x-component of the vector is Vx = -4.0 cm/s, while the y-component is Vy = 0 cm/s, assuming that only the negative x-direction component is provided.
Step-by-step explanation:
To find the x-component and y-component of the vector v = (4.0 cm/s, −x-direction), we must take into account the direction specified. Since the vector is in the −x-direction, the x-component will be negative. Thus, the x-component can be expressed as Vx = −4.0 cm/s. According to the information provided, there is no y-component mentioned for this vector, which would imply that Vy = 0 cm/s.
However, if we consider similar cases where a vertical (y) component is given, such as Vy = −24.5 m/s, and want to find the magnitude of the final velocity v, we would use the Pythagorean theorem: v = −(Vx² + Vy²). As an example, substituting Vx = 20.5 m/s and Vy = −24.5 m/s, we would obtain v = −((20.5 m/s)² + (−24.5 m/s)²).