Can an arrow fly 38km?

In the drama Mr. Sunshine,
A character fires an arrow from a place called Gosanjeong,
To Manhyujeong (a place where pottery is made).
The arrow flies approximately 38km at the speed of light..
What's even more amazing is that the female protagonist clearly aims toward the northeast..
Yet, miraculously, the arrow travels around the world and flies toward the south.