Math Is Fun Forum

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

the bird flies,and flies,and flies again.

Two trains travelling with constant speed V towards each other and distance between them is L initially.A bird is flying continueously between them with its speed V'.

1)Find the no. of times bird went to the other train and came back.
2)Find the time after which the trains meet.

I took out the time as L/2V.

Pls tell me about the first part.

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friendship is tan 90°.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: the bird flies,and flies,and flies again.

I guess we have to assume V' > V  or there's no question.

This means the bird can always go between the trains, even when they are close.  It looks like, in this idealised situation, the bird has an infinite number of shorter and shorter journeys.  I say idealised because we have to assume that it takes no time to turn around and go the other way, and that the gap is never so small that there's no space for the bird.

I hope that's right. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: the bird flies,and flies,and flies again.

Yes, if L' (length of the bird) is 0, it is an infinite number of times. If not, then it gets a bit more complicated. All I can say for that case is that after t=(L-L')/(2V) time, L' starts monotonically decreasing.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: the bird flies,and flies,and flies again.

yes it is infinity but I wanted to know how to frame equations for these type of questions.

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friendship is tan 90°.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: the bird flies,and flies,and flies again.

http://mathworld.wolfram.com/TwoTrainsPuzzle.html

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
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Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: the bird flies,and flies,and flies again.

hi Niharika,

Let's say the bird is at train A and about to fly towards B.  It's tricky as B is moving too.

One way to simplify the problem is to 'bring B to rest'.  Imagine a frame of reference which travels with B at V.  That effectively cancels out B's velocity so it is no longer a moving target.  But you must apply the same to train A and the bird.

new velocity for the bird = V + V'
new velocity for A          = 2V

At the moment the bird starts off, B is stationary at a distance L, so the time to reach B is T1 = L/(V+V')
and in that time A will have travelled 2VT1 so that the distance between the trains is now = L - 2VL/(V+V')

Now reverse the bird.  Bring A to rest, so that B is travelling at 2V and the bird again at V+V', but now in the other direction.

You can get an expression for T2, the time for the bird to travel to A, and calculate the new distance between A and B.

You should end up with a geometric series, for which you can calculate the sum to infinity.

The algebra gets pretty nasty which may be why Agnishom's link is to a numeric example.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: the bird flies,and flies,and flies again.

Hi Bob

Shouldn't the distance end up being finite? Maybe I've just misunderstood what you said.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: the bird flies,and flies,and flies again.

hi Stefy,

calculate the sum to infinity.

Did you mean this ?

It means

rather than

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: the bird flies,and flies,and flies again.

thanks bob.

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friendship is tan 90°.