5-year olds shouldn't circumnavigate alien planets

Susan is 5 Earth years old. She is also exactly 1 meter tall. On the planet Floobenweifer, there lives a race of aliens called Floobs that kills humans at night. To avoid the night, Susan walks faster than the planet is rotating, to keep ahead of sunset. The planet has a diameter of 500 kilometers, and she walks at 200 km/h. After completing a whole walk around the entire circumference of the globe, let $X$ be the difference between the distance Susan's feet go, and the distance the top of Susan's head goes. If $X$ can be expressed as $a\pi$ , find $a$ .

Details and assumptions

• Susan's feet never leave the ground.

• Floobenweifer is a perfect sphere.

• No Floobs or little girls were harmed during the making of this problem.

• Susan is an insane runner.