MathDB

A point is "bouncing" inside a unit equilateral triangle with vertices

(0,0)

(1,0)

, and

(1/2,\sqrt{3}/2)

. The point moves in straight lines inside the triangle and bounces elastically off an edge at an angle equal to the angle of incidence. Suppose that the point starts at the origin and begins motion in the direction of

(1,1)

. After the ball has traveled a cumulative distance of

30\sqrt{2}

, compute its distance from the origin.

Problem Statement