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The Falling Ladder Paradox

P. Scholten
Journal / Anthology

College Mathematics Journal
Year: 1996
Volume: 27
Issue: 1
Page range: 49-54

Anyone who has studied calculus has probably solved the classic falling ladder problem of related rates fame.... The standard solution model for this problem is to assume that the tip of the ladder slips downward, maintaining contact with the wall until impact at ground level, so that if the base and tip of the ladder at any time t have coordinates (x(t), 0) and (0, y(t)), respectively, the Pythagorean theorem gives x^2 + y^2 = L^2; see figure 1. ... The paradox in this solution is that as the ladder nears the ground, [dy/dt] attains astronomical proportions.

*Mathematics > Calculus and Analysis > Calculus

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