Bird flying b/w colliding trains

In summary, the problem involves two trains traveling towards each other on the same track at a speed of 25 km/h. A bird, flying at a speed of 60 km/h, starts at one train and flies back and forth between the two until they collide. The question is how far the bird travels before the collision. One way to solve this is by calculating the time until the collision and multiplying it by the bird's speed. Another way is to sum an infinite series of distances traveled by the bird. The problem is known for a story where a mathematician was asked this question and gave the correct answer by summing the series. The given problem assumes a constant speed for the bird and no turn-around time or wind.
  • #1
mbrmbrg
496
2
I'm sure there's already a thread about how else to solve the famous problem re: the distance covered by a bird flying between two trains on a collision course (other than adding up the sums, of course), but I can't find it.
Can anyone give me a quick link?
Thanks!
 
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  • #2
The elapsed time is how long it takes for the trains to collide from the starting point. Distance covered is the bird's average speed times the elasped time.
 
  • #3
It might be famous in the US, but I've sure never heard of it. What the hell are you talking about? :confused:
 
  • #4
One way to do this problem is to calculate distance the bird, after leaving the first train, must fly to reach the second, then the distance back to the first (taking into account the motion of the trains during the flights), etc. thus getting an infinite series to be summed.

The easy way is to calculate the time until the trains collide, the multiply the bird's speed by that time.

What makes it "famous" is that there is a story that a person once asked (Von Neumann, Weyl, Wiener, ... pick your favorite big brain) that question. The mathematician thought for a second and gave the correct answer. The first person chuckled and said "many people try to do it by summing an infinite series." At which (Von Neumann, Weyl, Wiener, ... ) looked puzzled and said "but I did it by summing an infinite series!"
 
  • #5
:rofl:
Okay, I see what the original problem was. Does the question assume a constant speed for the bird with zero turn-around time, or are positive and negative accelerations included?
 
  • #6
Jeff Reid said:
The elapsed time is how long it takes for the trains to collide from the starting point. Distance covered is the bird's average speed times the elasped time.

:hits self over head repeatedly:

Right... Talk about a brain twister. I knew there was an easy solution and I thought for SO LONG, and yet--

Well, thanks for untwisting my brain!
 
  • #7
Danger said:
:rofl:
Okay, I see what the original problem was. Does the question assume a constant speed for the bird with zero turn-around time, or are positive and negative accelerations included?
It does indeed assume zero turn-around time and constant speed throughout (and no wind :biggrin: ) which is why it can be done by just calculating he time until collision and multiplying this by the speed of teh bird.
 
  • #8
Sorry, Danger. Here's the problem as was given to me:

Two trains, each having a speed of 25 km/h, are headed at each other on the same straight track. A bird that can fly 60 km/h flies off the front of one train when they are 58 km apart and heads directly for the other train. On reaching the other train it flies directly back to the first train, and so forth. (We have no idea why a bird would behave in this way.) What is the total distance the bird travels before the trains collide?
 
  • #9
mbrmbrg said:
A bird that can fly 60 km/h flies off the front of one train when they are 58 km apart and heads directly for the other train. On reaching the other train it flies directly back to the first train, and so forth.
Not the most efficient way to play badminton, but I suppose it would be good for a laugh. :rolleyes:
 

1. How is a bird able to fly between colliding trains?

Birds have the ability to fly due to their specialized physical features, such as lightweight and aerodynamic bodies, strong and flexible wings, and efficient respiratory and circulatory systems. They are also able to adjust their flight patterns and maneuvers to navigate through tight spaces.

2. Is this scenario possible in real life?

No, this scenario is not possible in real life. Birds have excellent reflexes and spatial awareness, allowing them to avoid collisions with objects and other birds while flying. They would not intentionally fly between two colliding trains, as it would be a dangerous and fatal choice.

3. Can a bird get injured while flying between colliding trains?

Yes, it is highly likely that a bird would get injured or killed if it attempted to fly between colliding trains. The force and impact of the collision would be too great for the bird to withstand, and it would not have enough time to react and fly away.

4. What would happen to the trains if a bird flew between them?

If a bird flew between two colliding trains, it is possible that the trains could suffer minor damages such as dents or scratches. However, the trains are designed to withstand high-speed collisions and would most likely not be significantly affected by a bird flying between them.

5. Has this scenario been tested or observed in any way?

There is no evidence or record of a bird flying between colliding trains in real life. This scenario is purely hypothetical and has not been tested or observed. It is important to remember that birds are intelligent creatures and would not willingly put themselves in such a dangerous situation.

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