Co-ordinate Geometry - insect quest

1

Arshad ~Died~ ·2009-10-03 08:53:49

let us not let this thread die away without being solved..........
evryone pls tryyyyyyyyyyyyyyyy...............
nishant sir..........pls solve

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4

UTTARA ·2009-10-01 10:28:57

Sorry It's 2R sq instead of 4R sq in the pic !!!!!!!!!!

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1

RAY ·2009-10-01 10:37:48

u cannot move inside uttara...warna nishant bro ye question sayad hi post karte..lol

EVERYONE KNWS THE SHORTEST DISTANCE BETWEEN TWO POINTS IS A ST LINE..so dat wouldnt be apossible answer to such a long thread

ANOTHER QUESTION PERTAINING TO THE TOPIC

shortest path around cylinder
An ant starts at a point on the bottom edge of a right circular cylinder of radius and height . If the ant makes complete circuits around the cylinder and finishes at a point at the top edge directly above its starting point, find, with justification, the length of its shortest possible path.

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24

eureka123 ·2009-10-01 10:56:00

basically what mistake uttara is commitin is that she is moving the ant on straight line.....it wont move on stragiht line inside the cylinder..beczo of curvature..

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1

$ourav @@@ -- WILL Never give ·2009-10-01 11:00:39

Râˆš2 is obtained when we take the path across a chord which makes 90Â° at d centre of d circle...

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1

$ourav @@@ -- WILL Never give ·2009-10-01 11:08:18

if i take a case of values,my answer is smaller dan uttara...plz check

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4

UTTARA ·2009-10-01 19:22:36

@eureka123 : Do v need to consider the insect ???? In Nishant sir's Qs it's just mentioned to find the shortest dist b/w two opposite vertices on a cylinder !!!

@maths _psy : How R √2 I don't get u ? Which chord n circle r u considering?

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24

eureka123 ·2009-10-01 20:18:21

well I read teh topic of thread and replied.....If it is not insect then not much to wory..but if it is insect then we certainly cant go that way[6]

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1

aposlil ·2009-10-02 01:00:41

there is more to this question than it meets the eye

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1

Arshad ~Died~ ·2009-10-02 07:38:53

so nishant sir whats the answer..........????

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1

Arshad ~Died~ ·2009-10-02 07:40:31

everyone see this for hint
http://www.mathhelpforum.com/math-help/geometry/45778-shortest-path-around-cylinder.html

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23

qwerty ·2009-10-02 07:59:20

wat about the cube one ka answer??

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23

qwerty ·2009-10-02 08:18:43

i hav posted the ans already scroll up...i jus wana confirm..and confirmed!!

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1

RAY ·2009-10-01 10:05:23

can u move from inside the cylinder uttara?

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4

UTTARA ·2009-10-04 11:59:50

@xyz : Y do v need to open up the cylinder when v have no conditions like not travelling

inside I dont get ur point!!

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62

Lokesh Verma ·2009-10-04 22:45:54

Let me give a hint..

what uttara and maths_phys have done in post 28 and 19 respecitvely are correct.. (Both take a straight line)

But there is one small missing thing....

The final answer will depend on the function/. relation between r and L

Think about it?

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4

UTTARA ·2009-10-05 06:40:12

@Nishant Sir can we say the shortest distance is achieved at L = 4R ???????????/

i.e. shortest dist = √20R²

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62

Lokesh Verma ·2009-10-05 06:49:07

no uttara.. the way I think this will work.. is that

We have to compare 2R+L and √(piR)²+L²

which is 4R²+4RL+L² > (piR)²+L²
which is 4R²+4RL > (piR)²
0 > (piR-4L)R

0 > (piR-4L) (since R>0 always)
so if R<4L/pi

then you will have the first path

otherwise the 2nd path... [1]

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4

UTTARA ·2009-10-05 09:56:16

But Nishant Sir y do v need to compare 2R + L & √(piR)² + L²

I've considered √(2R)² + L² < √(piR)² + L²

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62

Lokesh Verma ·2009-10-08 07:34:28

Qwerty dont worry about pinked posts as much.. it is my request to all users here.. I kind of feel bad when i see that the motivation to interact here is the number of posts or number of pinked posts etc..

We are all here not to give or take more pinked posts but to learn new stuff.. Even I keep learning everyday here.. Believe it or not, I think that I am one person who has learnt most here!