071

Part of 1965 All Russian Mathematical Olympiad

Problems(1)

ASU 071 All Russian MO 1965 spaceship finds the inhabitant on planet

Source:

On the surface of the planet lives one inhabitant, that can move with the speed not greater than

u

. A spaceship approaches to the planet with its speed

v

. Prove that if

v/u > 10

, the spaceship can find the inhabitant, even it is trying to hide.