Anyone have time to input those 5 equations into Maple or Mathematica as I don't think there is any easy way of solving those 5 equations otherwise.
Looking at scale diagram, the answer should be around 5m mark
I would not ask this question if it was simple & I could do it myself !
It works out with 5 horrible equations with 5 unknowns :
Here is more detail posted elsewhere :
"this is a relevant track problem
it's about the curved start for races not 100 or 200 or 400
it's about the curved-line start...
I'm not proficient here, nor skilled, but it is it one of most important calculations in sport.
Every point on Mile start line means all run 1609.344m by hitting tangent at various points on 1st bend
Every guy has to hit a tangent at assumed different parts of bend
( 36.80m is shortest...
Can't find it here on search.
This caused huge rumpus when set as exam problem few months ago :
http://www.telegraph.co.uk/education/educationnews/11921671/Can-you-answer-the-tricky-crocodile-maths-question-that-left-students-in-tears.html
Solve
8 (b)
without Calculus...
I don't have much confidence/interest in your answer.
I want as much precision possible.
I have no interest in "energy rate".
Just 2 parameters with what 1500 is...
I'm interested only in 1500.
Don't bother with extreme distances above/below.
The answer is somewhere in 3'28-low region +/- tenths.
It is refining precision...
No
There is no world record for 1600m
No
I know it is a Log relationship from years of research/calculation
Then try some to link 1'42.00 for 800 with 3'44.00 for 1600
Thank you
I normally end up with 3'28.25 with my alternative attempts at solution, but I believe that may be 1 or 2...
I am interested in track & have found through some hard work that for 800 that 1'42.00 is same value as for 3'44.00 for 1600
( note : for 1600m not 1 mile )
It is a Log relationship but I can't quite settle on what the value for equivalence should be for 1500m.
I have a provisional figure of...
This is all very nice chat, but I'm not any closer to an answer.
Forget bunkers, lakes & Bill Murray's gopher ( ! )
I'm just thinking how driving 310 instead of 300 subtends a bigger angle of shot to a straight-ahead 4.25" diameter hole on a 500y straight hole & increased chance of...
I'd be interested in some input on a question asked by a friend.
Suppose you are a golf pro & train harder ( weight-training ) & increase your maximum driving ability from 300 yards to 310 yard with same accuracy.
What theoretical advantage is this likely to offer you on the course ...
Believe me, the relationship is cubic :
http://www.atm.ox.ac.uk/rowing/physics/basics.html#section5
Use that.
Try & see if an empirical relationship using cubic relationship for energy &/or the suggested range of times above is obvious ( Maple or Mathematica ? Or just plain...
We are looking for "equivalent" performances for the main middle distance & distance track races : 800m, 1500m, 3000m.
For some guidance, it is generally reckoned that a 13'00 or a 27'10 is in ballpark of
800m : 1'43.5 +/- 1.0s
1500m : 3'31.0 +/- 2.0s
3000m : 7'30.0 +/- 5.0s