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 ℓ (in meters) it may turn through for any acute angle α such that tanα<1000ℓ. 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. trigonometrycombinatorics unsolvedcombinatorics