Squishing a Semi-arc
An arc is suspended between two lines at fixed points \(A\) and \(B\) on the line such that segment \(AB\) is perpendicular to both of the lines. The arc has length 100 units and segment \(AB\) has length 90 units. The two lines move closer and closer at a rate of 2 units per minute, thus squishing the arc. After how many minutes does arc \(AB\) no longer become an arc?
Details and assumptions
Arc \(AB\) obeys physical properties, and bends in the most natural way possible
Arc \(AB\) never goes through either of the lines suspending it