Taking the pole into the room (in 3D)
Ok, no one has figured out the required hallway width.
Remember this...
"The pole from the previous flatland post, is now going
into a large room off a hallway. The walls are 6 inches thick,
the door is 30 inches wide. The pole is 24 feet long.
The hall is not very wide. How wide would it have to be for
the 4 inch diameter pole to be taken into the room without bending it?"
Now assume we are not in flatland. The door is 7 foot high, the ceiling
in the hall is 8 foot high. What is the hallway width required if we can tilt
the pole?
Remember this...
"The pole from the previous flatland post, is now going
into a large room off a hallway. The walls are 6 inches thick,
the door is 30 inches wide. The pole is 24 feet long.
The hall is not very wide. How wide would it have to be for
the 4 inch diameter pole to be taken into the room without bending it?"
Now assume we are not in flatland. The door is 7 foot high, the ceiling
in the hall is 8 foot high. What is the hallway width required if we can tilt
the pole?
posted by Ragknot at
5:45 AM
9 Comments:
R U confident that you know the answer to this and previous version?
I'm not doing it as it requires too much effort.
The answer to the previous problem was 86.9107 inches or about 7 feet 3 inches. The only hard part of it was constructing a line tangent to a 4 inch circle to find the correct angle. That angle would used here also, but tilting the pole would effectively shorten the 24 feet.
Sounds way too big. But only because of my lazy answer to the previous. Was my answer that far out?
Is the end of the pole flat or round? I just assumed that the ends were flat (in the previous question) i.e. that the pole was a rectangle. If the ends are semicircles (or hemispheres in this problem), it sounds likely to be a major nightmare to solve in either problem.
In flatland, the pole is a rectangle 24 ft by 4 inches.
But for this post you could assume that it is a cube 24ft x 4inch x 4inch and get the same answer.
I'm pretty sure you're right about it not mattering, whether the pole is round or square.
I also suspect that the problem isn't quite such a nightmare as I first thought.
But too much fiddly trig and coordinate geometry for my little head.
Ragknot, as it's you, I'll have a go at your problem so you won't have to yell at me.
Ragknot, change of heart. Started looking at 3D version and decided it was far too difficult to visualise or draw. So I'm not going to try. Soz.
Solutions to my posts about taking the 24 foot pole from the hallway into the room are here.
http://ragknot.blogspot.com/
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