Alien vs Alien Hunter Puzzle I found this puzzle posted on a student website I frequent, but no one including the poster nor I could solve it. So I'm posting this puzzle here with hope that some of math whiz in here could illuminate on how to approach it: > There is an alien on the surface of a spherical planet. The alien can run at a top speed of $u$. An alien hunter is hunting the alien in his spaceship which can fly at a top speed of $v$. Once the hunter sees the alien, he fires, and the alien dies. Show that the alien will always die if $v > 10u$. Note that there's no information given about the planet radius nor the altitude at which the spaceship hovers so I'm suspecting that the solution somehow ignores them or they get canceled out somewhere in the calculation. p/s: again I repeat that I do not know of the solution myself

Let us measure distance in planet radius and time such that the alien can make one radian per unit time on the surface. If I fly along the surface at altitude h, I can see a swath of width $2 \arccos (\frac{1}{1+h})$ and can fly around the equator in $\frac{2 \pi (1+h)}{10}$, so as long as $2 \arccos (\frac{1}{1+h})-\frac{2 \pi (1+h)}{10} \gt 0$ I can make a spiral starting at one pole and push the alien in front of me down to the other pole. At h of about 0.55, this only requires my speed to be about 5.6 instead of 10.