The Falling Ladder Paradox
The Falling Ladder Paradox
Authors: Scholten, Paul and Andrew Simoson
College Mathematics Journal, Vol. 27, no. 1, pp. 49-54, 1996
An assumption in the familiar related rates problem of the falling ladder is that the top of the ladder stays in contact with the wall the entire time the ladder is falling. However, when the base of the ladder is sliding away from the wall at a constant rate, the top of the ladder eventually loses contact with the wall. The authors use differential equations to model the situation when the top of the ladder starts out in contact with the wall but eventually loses contact with the wall. The path of the top of the ladder is graphed using Mathematica.