Bird Flies Between Two Trains Crashing at 60m/s

[neutrino']

two trains approach each other at 60m/s the gap between them is 120 m. A bird on one train flies to the other in 120m/s. The bird flies back again. But how many trips would the bird do before the trains crash?

thx

 

[MrB8rPhysics]

Is this 60 m/s the velocity of both trains relative to the earth, or relative to each other?

 

[skeptic2]

What kind of bird?

 

[MrB8rPhysics]

An unladen african swallow.

 

[skeptic2]

An unladen African swallow's top speed is about 18 m/s. What kind of bird can fly at 120 m/s (268 mph)?

 

[neutrino']

60 m/s relative to the earth. And the type of bird doesn't matter! It just travels 120 m/s

 

[MrB8rPhysics]

Some kind of birdplane? Or bird of prey in a steep dive.

 

[neutrino']

Some kind of birdplane? Or bird of prey in a steep dive.

all that doesn't matter! ok asume it is a particle which can "fly" from one of the train to the other and backforth

 

[zachb657]

Im taking a guess! Correct me if I am wrong! 2 Sec's? 120 ms to 120ms back?

 

[neutrino']

by the way the trains crash 1 sec after they start their motion.

 

[MrB8rPhysics]

I have done a crude from first principples method that suggests that there could be an infinite number of stops made by the bird (transit time for the bird between the trains drops exponentially). This however feels silly, and I gave up pursuing the method after I established that the bird would be landing for third time returning to its start point after 0.975 seconds while the trains were 9m apart (thats 4.5 m from the point of impact). The bird will probably be able to make a return trip over that diminished distance before the trains impact, but I haven't done any work to prove so.

 

[neutrino']

have you assumed the fact that after the bird started flight the destination train gets near the bird?
as you said infinite stops is wrong because it implies that the trains don't collide!

 

[MrB8rPhysics]

Yes I have taken the motion of the trains into account. I am trying to get my head around how to come up with a raw number in a more elegant way than simply chunking it down into smaller and smaller time iterations, waiting for the bird to not have enough time to get between the 2 trains as they close. I have a gut feeling the answer is 2 complete and one incomplete transit. But can't prove it... yet.

 

[neutrino']

i came up with:

summation of [(2)/(3)^b] equals 1.

where b is the number of stops.

 

[neutrino']

I am not able to solve this equatio, b becomes infinity!

 

[MrB8rPhysics]

Yea, which is the problem I have run into, especially if we assume the bird takes zero time to change direction - it is always moving faster than the trains and has an ever decreasing distance to cover. I tried plotting the displacement of all objects from the colission point and ended up with a nice pattern - 2 lines of constant gradient for the motion of the trains, and a line for the motion of the bird with the correct relative gradient, and simply ended up with a recursive zigzag for the bird that seemed to be going fractal. I am very tempted to actually programme this into some kind of simulation to see what should happen and work backwards...

 

[neutrino']

oh please do programme a simulation, they help a lot. I haven't learned programming.
Can you explain what you plotted? (the gradients)?

thx

 

[Delphi51]

Looks like a Zeno's paradox.
The computer can't go much further without running into calculation problems with the small numbers.

 

[DaveC426913]

Yes. It is simply a convergent series. It has infinite elements yet sums to a finite number.

Same as 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... = 2.

 

[neutrino']

so what is the conclusion? does it literally mean infinity "exists"? because afterall the trains must crash. But infinity doesn't exist

 

[MrB8rPhysics]

In reality, the bird won't have an instantaneous change in direction - it will eed to decelerate and accelerate gain, meaning a finine number of transits. This model doesn't account for that.

 

[neutrino']

In reality, the bird won't have an instantaneous change in direction - it will eed to decelerate and accelerate gain, meaning a finine number of transits. This model doesn't account for that.

So let this problem be out of reality (assumming instnataneous change in direction). Then what does it imply?

 

[MrB8rPhysics]

Infinite transits of the bird, as it is always moving faster from train to train than the trains move together, regardless of the idstance between the 2 trains.

 

[Delphi51]

Zeno's paradox (the way I first heard it!) is about a man crossing a room to meet a beautiful woman. It takes 1 second to get half way across the room, 1/2 a second to go half the remaining distance and so on...
1 + 1/2 + 1/4 + 1/8 + 1/16 + ...
At this rate it appears it might take an infinite amount of time to reach the woman.
As my friend said, "He will soon be close enough for all practical purposes."
And mathematics says the total time is 2 seconds.
In the train problem, the trains crash in 1 second. The bird with infinite acceleration does make an infinite number of trips between trains during this second - but it must be infinitesimally small and have a mass of zero to accomplish the feat.

 

[neutrino']

so it isn't conclusive proof that infinity exists? I mean the trains crash but how come the particle (the bird with ~0 mass) make inifintely many stops? THE TRAINS CRASH, RIGHT??

 

[Delphi51]

The bird goes from 120 m/s one way to 120 m/s the opposite way instantly. It never stops. Yes, the trains crash. They are behaving normally, moving in constant speed motion. The bird is not moving according to physical laws; hence the infinite number of passages.

 

[SammyS]

Well, the bird flies a finite distance, in a finite amount of time, but does that in an infinite number of intervals !

 

[DaveC426913]

Convergent series are those that have an infinite number of elements, yet sum to a finite number.

As the infinite sequence 1/1 + 1/2 + 1/4 ... sums to the finite value of 2, so too does the bird's infinite transits sum to a finite duration of time.

 

[PeterO]

so it isn't conclusive proof that infinity exists? I mean the trains crash but how come the particle (the bird with ~0 mass) make inifintely many stops? THE TRAINS CRASH, RIGHT??

It was important what sort of bird!
If it was a sparrow, which is about 10cm long, then the trains will begin to squash the bird when they are 10 cm apart
If however it was a swan, which is about 1m long when in flight ...

 

[damnwebassign]

i came up with:

summation of [(2)/(3)^b] equals 1.

where b is the number of stops.

b=[log(2)/log(3)]

 

[PeterO]

so it isn't conclusive proof that infinity exists? I mean the trains crash but how come the particle (the bird with ~0 mass) make inifintely many stops? THE TRAINS CRASH, RIGHT??

Once we add in assumptions that the particle has no dimensions, nor mass - so that the train don't both contact the particle until the trains are also touching each other - and the particle ca also change from velocity in one direction to velocity in the other direction [ie have infinite acceleration] it is not surprising that the number of trips the particle makes in infinite - but then only the first half of the infinite trips took any real time - the rest of them were done in an infinitely small time interval, perhaps?

 

[DaveC426913]

so it isn't conclusive proof that infinity exists?

What does one man by "exist"? Is it a useful tool in mathematics? Absolutely. We just used it in one.

Does it exist in some physical way? This experiment gets us no closer to an answer, since this is so clearly an unphysical thought experiment (zero mass, point-sized birds and such).