OT : A "Lockdown" Puzzle
- Thread starter daba
- Start date
Peter Nachtwey
Member
Yes, it was Christmas 2010!. you can see the date on my pdf file.
https://deltamotion.com/peter/Mathcad/Mathcad - rabbits.pdf
I solved the the problem using different techniques.
I must be getting old, time starts to run together or be compressed.
This was a little more challenging than trains and tunnels.
Lockdown Puzzle : Rework
I feel the figures in my original "puzzle" were a little too easy to work with, so here goes for Round 2, with a twist !
The train is now 575 yards long.
The tunnel is now 4.3 miles long.
The train clears the tunnel, nose in to tail out, in 10 minutes.
What average speed through the tunnel was it traveling to achieve this ?
(Answer via PM, to 2 decimal places will be adequate)
For those who built an excel spreadsheet for this, and depending on how you built it, there may be some circular referencing going on, deal with it...
I feel the figures in my original "puzzle" were a little too easy to work with, so here goes for Round 2, with a twist !
The train is now 575 yards long.
The tunnel is now 4.3 miles long.
The train clears the tunnel, nose in to tail out, in 10 minutes.
What average speed through the tunnel was it traveling to achieve this ?
(Answer via PM, to 2 decimal places will be adequate)
For those who built an excel spreadsheet for this, and depending on how you built it, there may be some circular referencing going on, deal with it...
drbitboy
Lifetime Supporting Member
- Definitely 32, because if they travel dL (differential-L) in a straight line, then they are [dL x 2**-0.5] closer to the center.
- They are always moving at 45degrees to the right of [the vector from themselves toward the center of the square.]
- Inverting: they travel dR*2**0.5 in a straight line to get dR closer to the center
- δL/δR = 2**0.5
- Since they started 2**4.5 (=16sqrt(2)) from the center,
- that 2**4.5 is how much closer they must get to the center to reach the center (integral of dR)
- ΔR = 2**4.5
- So their total straight, but infinitely small, line segments' movement
- ΔL = ΔR x δL/δR
- = 2**4.5 x 2**0.5
- = 2**(4.5+0.5)
- = 2**5
- = 32
- ΔL = ΔR x δL/δR
P.S. Characterizing the travel toward the next rabbit is a canard, even if it does lead to an approximate solution; this is the same class of problem as the bird flying back and forth between two trains traveling toward each other; of course John von Neumann allegedly solved it by doing the infinite sum as quicker than others saw the trick.
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drbitboy
Lifetime Supporting Member
Of course, whether they get to the center depends on whether they are engineer rabbits or mathematician rabbits.
Because when put in the diagonal corner of a room opposite to his wife and told to kiss her but that he could only step half (or 70.7...%) of the way to her at a time, the mathematician sat down and cried.
Meanwhile the engineer started stepping away because he knew he could get close enough for all practical purposes.
Because when put in the diagonal corner of a room opposite to his wife and told to kiss her but that he could only step half (or 70.7...%) of the way to her at a time, the mathematician sat down and cried.
Meanwhile the engineer started stepping away because he knew he could get close enough for all practical purposes.
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What is the twist ? I dont see the need to use Excel for something like this.
Just normalise your dimensions and then you have a very simple equation of distance over time gives you the velocity.
Maybe the train is going backwards?
geniusintraining
Lifetime Supporting Member + Moderator
I did not spend a lot of time on it but in the PM you said my answer was wrong... so whats correct answer and how was it calculated? I broke mine down to seconds then tried to figure it out
Would this be the Swedish train tunnel that has a station inside?
Then we would need to know the deceleration and acceleration rates along with the stopped time.
Or, if not a station, the speed limit change at the internal curve.
That was your problem. Should have used yards/fortnight..
bernie_carlton
Lifetime Supporting Member + Moderator
My physics teacher in high school when teaching about units conversions had us convert the speed of light to furlongs per fortnight.
It was with a little joy and a grin when I just realized that the "S" in PLCS.net stands for SarcasmPeter Nachtwey
Member
This is a first year algebra "story" problem. Did anybody get it yet?
My Mathcad will do the units conversions for me so this is not a challenge.
My Mathcad will do the units conversions for me so this is not a challenge.
The state of Michigan implemented years back an exam that had to be passed to get a standard high school diploma.
Now, everyone I have ever known up for a diploma was a high school senior - but the state legislature had a BIG problem deciding whether to make the test at the 6th or 7th grade level. It was never even considered to make the test at a high school level, especially a high school senior year level.
I have met college educated professional engineers that have asked questions that I think the average middle school student should know - and even asked one if he skipped that day in engineering school when they taught how gears worked. (He stated the gear next to the one he had a problem with was going backwards)
Peter Nachtwey
Member
We don't want the little angels to have to live with the stigma of failing high school do we? So we only fail those that are too stupid to not care.
Reality check. Life is one long test.
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