1this one is marvellous !!!!!
RR' is a road on which Powerplant P has to be constructed.
There are two villages A & B on same side of the road.
Find the optimum location of poweplant P such that wiring cost i.e. PA+PB is minimum.
Note: You should not use differentiation. Think Physics.
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30 Answers
62btw once u know it is a reflection, this is the obvious step :P
1why has no one mentioned a small remark .. a proof that the minimum distance will be the path shown above ..
Simple geometry does much better here than Fermats principle
1yes gr8 and thanx evryone for their contributions in thi s one i got similar q in a test and i solved it in a minute while the others were pining out long differentiations[4]
thanx
62
This image the reflection is shown..
Do u realise that the line (Red) are straight lines!
So u need to refelct the points A and B and take straight lines joining A and B' or (B and A')
Abhishek.. use this method in the question u asked..
http://www.targetiit.com/iit_jee_forum/posts/ftse_questions_190.html
It will solve it in a flash!! It took me 30 seconds flat to get the point on the x axis (Not bluffing :D)
62Guys u have all posted the answer.. but i dont think anyone got to the method i wanted..
I know there are a few hours to go today.. But inspite of the fact that Priyam infact got the reflection part of my Hint (Think Physics).. no one got the actual method that i wanted to see..
U guys did get a very good solution though..
I think i will post the solution.. now itself :)
62hey that is a great work to look at it that way as well :)
It gives u gr8 insight into the whole thing... specially if u want to confirm that this is indeed true :)
1heyyyyyy!!!
i did something jus' now!!!
(it was nishant bhaiya's idea tho.. )
i took a thread...
drew a strait line (the road) and the two villages as in figure...
took the minimum length string (considred dat from P slopes are equal for the minimum length..)....
then marked dat point...
as i moved the point P(position of the pole) at some other place on the road,,,, the string was falling short of length.... it was not reaching the villages...
... this means they need longer threads...
....this means the one with equal slopes is shortest... :)
...tho it was obvious but nice experimenting... :)
62hmm.. gr8..
this is good solution.. a perfect one :)
Side note: u guys realised that it was reflection.. but no one reflected actually :D
1
was thinking dat the two angles will be same but had no reasons... but abhisekh has given the point...
so ,, slope of AP= slope of BP.
=> a/(-p) = -b/(d-p)
=> ad - ap = bp
=> p= ad/(a+b)
1construct two perpendiculars from A and B touching the road RR' at M and N respctivly...
let MP=x... then, PN=d-x
AP2= a2+x2..
BP2= b2 + (d-x)2
AP + BP = √a2+x2 +√b2 + (d-x)2 = Y(say)
we will find minima of Y...
but this will get long ... must be some finer method... will think...
62yeah i am looking for a "slighty" better solution that gives a far better insight into the whole stuff :)
1Let the distance be x from r then :
a/x = b/(d-x)
x = ad/(a+b)
Dist from R is ad/(a+b)
33What i did was to make tanθ equal in both ΔAMP and BNP......
Similar triangles only...
62btw can i have ur solutino.. cos i still think u dont have the "best" solution!
i mean u will be around 80%-90% correct..
but the solution that i really want to see could just stump that problem u just mentioned!!
33Well this q has opened my mind 4 other questions of the same kind gr8
earlier it took wholesome diff but know it will be eay.....
This questions is gr888888 :)
62Hey cool.. this works very fine with the same logic :)
Gr8 one that u pointed out priyam..
dont know if u could work that out this way?
33Posted something there:
Forum » Fundamentals » FTSE questions.........
http://www.targetiit.com/iit_jee_forum/posts/ftse_questions_190.html
62hmm.. this is an interesting point..
i think it could work as well.. but we need to figure out the reflections properly!
I cant immediately.. but lets see if we can get somethign gr8 for that as well :)
33Hey is this will be true for the question 1 of Link below:
but theres PA+PB+AB
that AB extra so will this work there also....
Forum » Fundamentals » FTSE questions.........
http://www.targetiit.com/iit_jee_forum/posts/ftse_questions_190.html
33Is the answer x=ad/(a+b)?
x is dist frm base of A
and this answer is very common in COM's and Many others
33I think it should be such that light from A after reflection from RR' pass through B.....
Light usually travel min possible with min possible time and here c is same so that will be for min dist...........
Actually i read one writeup on this on snell's law in NCERT any one wishing to take min time should follow snell's law when tavelling from one med 2 other having diff velocity...
so i though this should be true for this case for reflection also.......
Yes. Thats y the question has been posted.
I have added a note [1]
Note: You should not use differentiation. Think Physics.