MathDB

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.

Problem Statement