MathDB

A fire that starts in the steppe spreads in all directions at a speed of

1

km per hour. A grader with a plow arrived on the fire line at the moment when the fire engulfed a circle with a radius of

1

km. The grader moves at a speed of

14

km per hour and cuts a strip with a plow that cuts off the fire. Indicate the path along which the grader should move so that the total area of the burnt steppe does not exceed: a)

4 \pi

^2

; b)

3 \pi

^2

. (We can assume that the grader’s path consists of straight segments and circular arcs.)

Problem Statement