What is the length of the longest rod that can get around the corner? HELP!

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tmillermillert

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A corridor of width a is at right angles to a second corridor of width b. A long, thin, heavy rod is to be pushed along the floor from the first corridor into the second. What is the length of the longest rod that can get around the corner?

The answer in the back of the book is ( a ^ ( 2 / 3 ) + b ^ ( 2 / 3 ) ) ^ ( 3 / 2 ).
It also says convince yourself that this and the preceding problem are essentially the same.

The preceding question is referring to the question below.

(The fireman's problem) A fence a feet high is b feet from a high burning building. Find the length of the shortest ladder that will reach from the ground across the top of the fence to the building.

Chapter Applications of Derivatives
Section: Applied Maximum and Minimum Problems
 
tmillermillert said:
A corridor of width a is at right angles to a second corridor of width b. A long, thin, heavy rod is to be pushed along the floor from the first corridor into the second. What is the length of the longest rod that can get around the corner?

The answer in the back of the book is ( a ^ ( 2 / 3 ) + b ^ ( 2 / 3 ) ) ^ ( 3 / 2 ).
It also says convince yourself that this and the preceding problem are essentially the same.

The preceding question is referring to the question below.

(The fireman's problem) A fence a feet high is b feet from a high burning building. Find the length of the shortest ladder that will reach from the ground across the top of the fence to the building.

Chapter Applications of Derivatives
Section: Applied Maximum and Minimum Problems
Click to expand...

This is a pretty standard problem in many calculus texts. The rod will fit only if it just barely grazes the inside corner. This gives you a method of determining the constraint. One method of solution involves exploiting the similar right triangles that form with the rod and the corridor walls, another you can use trigonometry for. I suggest you draw a diagram and come back with your thoughts on it.

I personally think the ladder problem is a bit simpler to think about. But depending on how you do it, the initial setup can be the same as the rod-corner problem, with the top of the fence taking the place of the inside corner of the hallway.
 
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