If the sun is beginning to set, how fast do you have to move west to prevent it from ever setting?

 Certainly!

To halt the apparent setting of the sun, one would need to match the rotational speed of the Earth. The Earth rotates from west to east, completing a full rotation roughly every 24 hours. At the equator, the speed due to this rotation is about 1,670 kilometers per hour (1,040 miles per hour). So, to counteract the sunset, an individual would have to move towards the west at this same velocity.

However, it's crucial to note that this theoretical pursuit presents a practical impossibility. Achieving and maintaining such an incredible speed for an extended period is beyond the capabilities of current human technology. Furthermore, the Earth's atmosphere, terrain, and various other factors would pose insurmountable challenges, making it impractical for a person to match the Earth's rotational speed.

Even if one could somehow manage to move at this speed, the curvature of the Earth would eventually come into play. As you move westward at that rapid pace, the curvature of the planet would lead to an altered perspective. Eventually, you'd encounter obstacles, such as mountains, bodies of water, or other geographic features, which would impede further progress, preventing the sun from perpetually remaining in the sky.

In essence, while the idea of chasing the sunset to prevent it from occurring seems intriguing, the immense speed required, coupled with the physical limitations and obstacles presented by the Earth's surface, renders this concept purely theoretical and unachievable in practical terms.