Solve The Ant Problem

The_Big_K

Got this problem from a friend through IM. Solve it !

Quote:

An ant is at a fixed end 'P' of a 1 meter-long rubber band.
Just as the ant starts walking along the rubber band at a constant 1 cm/sec,
the other end 'Q' is pulled away from 'P' at a steady speed of 100 cm/sec.

Assume a uniformly stretching, infinitely elastic rubber band is used in this puzzle.

Will the ant ever reach 'Q', and if yes, when?

-The Big K-

crook

To the best of my knowledge, the problem was discussed in Mindsport section of TOI! heck I don't know the answer.

I think the ant should take infinite time to reach the other end.

Rocker

Since the ant is located on the rubber, the total distance that the ant has to cover is just 100 cm. The total time taken will be 100 cm / 1 (cm/sec) = 100 sec.

LORD_EC

@the_big_K
Is the answer given by rocker is correct ???

This is what i think.
The aunt is at a fixed point P.Now the other end,Q is moving away from aunt(or point P) at the speed of 100 cm/sec.So in one second,the point Q will be 100cm that means Q is now 200cm apart from P.And after one more second,it will be at 300cm apart.Thus the distacne PQ will go on increasing.And the speed of aunt is not sufficient to compensate for that.

Am i right or am i misinterpreting the puzzle.
Anyone please clarify..

ankitvirmani

This problem can be correlated to a person walking@1m/s on a 100m long train.the person will cover the length of the train in 100s irrespective of the speed of the train.
Now people will say that here the entire rubber band is not moving, it is getting stretched.Hence the ant which is moving at an absolute speed of 1cm/s will be assisted by the stretching of the rubber band (increasing its absolute speed) and will cover the distance in 100s.(the increasing of speed can be justified if you look at stretching on a microscopic level)

satheesh27887

The ant never reaches the end Q.....
bcoz the band is infinitely elastic rubber band......
So it keep on stretches......

Do u think, It is correct??????

kidakaka

The problem has not been interpreted correctly. Assuming uniform elasticity, the length of distance the ant has to cover is increasing by 100 cm/s ... but please note, that in the first second, the ant has covered 1cm, the band is 200cm long ... and the ant has covered 2cms (since that 1cm is now 2cm ... due to stretching!!).

Then the ant goes ahead by 1cm, the band becomes 300cm long .. the distance behind the ant is 5cms. Then it goes ahead by 1cm, the band becomes 400cm long ... the distance behind the ant is 8 cms ahead.

Time Distance Covered %age
----------------------------
1 100 1 1%
2 200 3 1.5%
3 300 5 1.66%
4 400 8 2%

Looks like the ant is making some progress after all

. I say it will reach the end. And you know what ...

Moral of the story - Determination gets you there.

banu

no it won't reach Q
bcoz it will fall down as the band is stretched.
banu

anuragh27crony

Yeah i agree with the solution provided by Kidakaka...

Since the rubber is uniform ....so the distance travelled by the ant also get's streched.....