[ExI] mrs claus problem, was: RE: far future

[spike]

>. On Behalf Of Ben Zaiboc



Spike claimed:  "... so she turns right pi/2 ..."

 

>.Spike, NOBODY turns right pi/2  :D

 

I do, nearly every day.

 

>>."If Mrs. Claus travels 4 km north, then 3 km east, what is the maximum
distance she can be from the igloo?"

 

>.5km, because east is 90 deg. from north, and the ground is flat over such
short distances, and if she started out less than 4km from the north pole,
she'd get stuck there, according to those directions, because once you get
to it, you can't go any farther north.

 

On the contrary, sir.  Read on please.

 

>.Ha!  Take that, maths-boy!  Ben Zaiboc

 

If the term "that" represents "the derivative of the distance function" I
did so.  I took the derivative, set it equal to zero, solved for theta.
Rather attempted to.  Note the figure below, with Mrs. Claus' path in red:

 

_______________________________________________

 

 



 

The challenge is to find theta such that the distance from start is
maximized given a path length of 7 (or the more general N+E).  I can get up
to about 6.274 km, with a theta of about 2.01695.  (This is about 115.56
degrees, for the degree fans among us.  Note that degrees are in short
supply in the north pole region, even in our current era of global warming,
and even if you can find some, most of them are negative.) 

 

spike

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