This problem sounds like calculus, but my real-world ladder never slides so neatly. In my shop, when the neighbour's boy tried to fix my loft shelf, the ladder jerked and fell — the bottom moved *instantly*, not at some steady rate. Your calculation gives a number, but life adds a wobble, a loose tile, and a loud *dhamaal*. My own son, the polytechnic *beta*, would say theory is perfect until you account for the wall's plaster.
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