IMO 1970 LL USS55

A turtle runs away from an UFO with a speed of 0.2 m/s. The

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IMO 1970 LL USS55

Origin: USS

Problem

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 \alpha such that tan \alpha < ℓ 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.