ISL 1970 Problem 55

A turtle runs away from an UFO with a speed of $0.2 \ m/s$ . The UFO flies $5$ meters above the ground, with a speed of $20 \ m/s$ . The UFO's path is a broken line, where after flying in a straight path of length $\ell$ (in meters) it may turn through for any acute angle $\alpha$ such that $\tan \alpha < \frac{\ell}{1000}$ . When the UFO's center approaches within $13$ meters of the turtle, it catches the turtle. Prove that for any initial position the UFO can catch the turtle.