In calculus there are a number of problems called ladder problems. The most famo

Question

In calculus there are a number of problems called ladder problems. The
most famous is the related rates problem involving a ladder sliding down
the side of a building. Another problem involves moving a ladder down a
hallway and around a corner. That is the problem that we will tackle
here. We make the following assumptions about the situation we are
modeling:

The hallway has a width of 1.

The ladder has negligible width.

The ladder must be kept parallel to the floor.

The hallway has uniform width (except at the corner itself).

The hallways are sufficiently long and have no doors nearby that
could be used to move the ladder into.

A natural question to ask is what is the longest ladder that can be
moved around the corner. Your task is to solve this problem for the
following two situations:

1. The hallway turns a corner of 90 degrees.

Explanation / Answer

the problem is solved here: http://archives.math.utk.edu/visual.calculus/3/applications.2/ you are in the case with p=q=1 so lmax=(1+1)^(3/2)=2^(3/2)=sqrt(8)

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