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A Ladder Will Fall Infinitely Fast when Pulled

Consider a ladder of length L leaning against a frictionless wall which is at right angles to the ground. You pull the bottom of the ladder horizontally away from the wall, at constant speed v. The claim is that this causes the top of the ladder to fall infinitely fast.

Common sense tells us this can't possibly be true, but can you find the flaw in the following supposed "proof" of this claim?

         || \ L
         y|  \
         ||   \
         ||    \ =======> speed v
        ------------------------------------ ground
The Fallacious Proof:

See if you can figure out in which step the fallacy lies. When you think you've figured it out, click on that step and the computer will tell you whether you are correct or not, and will give an additional explanation of why that step is or isn't valid.

See how many tries it takes you to correctly identify the fallacious step!

This page last updated: May 26, 1998
Original Web Site Creator / Mathematical Content Developer: Philip Spencer
Current Network Coordinator and Contact Person: Joel Chan -

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