Please help with a trig optimization word problem.

Mar 2017
5
0
Canada
I'm not even sure what the diagram would look like for this:

A ladder 9m long is to be moved horizontally around a 90 degree corner from one corridor 2.5m wide into a second corridor. How narrow can the second corridor be and still permit the ladder to go around the corner? Neglect the width of the ladder.

The answer is 3.92m. Thanks in advance!
 

SGS

Mar 2015
38
7
Clarion, PA
I'm not even sure what the diagram would look like for this:

A ladder 9m long is to be moved horizontally around a 90 degree corner from one corridor 2.5m wide into a second corridor. How narrow can the second corridor be and still permit the ladder to go around the corner? Neglect the width of the ladder.

The answer is 3.92m. Thanks in advance!
You can't neglect the width of the ladder!

It depends on if you hold the ladder so the rungs are horizontal or vertical.
 
Mar 2017
5
0
Canada
It says you're carrying the ladder horizontally, so the ladder would be on its side if that makes sense.
 

Plato

MHF Helper
Aug 2006
22,506
8,663
I'm not even sure what the diagram would look like for this: A ladder 9m long is to be moved horizontally around a 90 degree corner from one corridor 2.5m wide into a second corridor. How narrow can the second corridor be and still permit the ladder to go around the corner? Neglect the width of the ladder. The answer is 3.92m.
You can't neglect the width of the ladder!
It depends on if you hold the ladder so the rungs are horizontal or vertical.
Only the length matters.
Look at the diagram.Untitled.gif

BTW. I once was at a University where the civil engineers of all people built a new building. Then they had custom made cabinets done. But the cabinets could not be moved in because they would not round the corners. Those of us who taught their students calculus had great fun when coming to this very question.
 

romsek

MHF Helper
Nov 2013
6,828
3,073
California
Only the length matters.
Look at the diagram.View attachment 37415

BTW. I once was at a University where the civil engineers of all people built a new building. Then they had custom made cabinets done. But the cabinets could not be moved in because they would not round the corners. Those of us who taught their students calculus had great fun when coming to this very question.
This is of course correct for this problem.

In real life you can also rotate the ladder parallel to the walls and gain a fair bit more leeway.

I know this from having done painting and having had to move ladders all over the place in narrow corridors.
 
Mar 2017
5
0
Canada
Only the length matters.
Look at the diagram.View attachment 37415

BTW. I once was at a University where the civil engineers of all people built a new building. Then they had custom made cabinets done. But the cabinets could not be moved in because they would not round the corners. Those of us who taught their students calculus had great fun when coming to this very question.
Thanks man. I managed to solve the question thanks to your diagram.
 

Plato

MHF Helper
Aug 2006
22,506
8,663
This is of course correct for this problem.
In real life you can also rotate the ladder parallel to the walls and gain a fair bit more leeway.
I know this from having done painting and having had to move ladders all over the place in narrow corridors.
Well try that with 600 lb. cabinets that are 11 meters long.