The bird's got some guts

  • Thread starter Rainbow
  • Start date
In summary, the problem asks for the number of trips and time taken for a bird flying between two trains to sandwich between them as they approach each other. While the number of trips may be infinite, the time taken is finite and can be calculated by considering the speeds and distances of the trains and the bird. An anecdote about mathematician John von Neumann highlights the misconception of summing an infinite series to solve the problem. The correct approach is to calculate the time it takes for the trains to crash into each other, which is L/2v, and the distance the bird flies in that time, Lw/2v.
  • #1
Rainbow
62
0
Here’s a question that I’m stuck with.
Two trains initially separated by distance L are heading towards each other on the same track each with speed v, and a bird flies from train A towards B with constant speed w>v reaches train B and immediately comes back to A with same speed and continues to do so till it sandwiches between the two. Find out the number of trips and time taken before it sandwiches.
I solved it mathematically and got the answer as infinity, which I find hard to accept. I think this is due to the wrong mathematical approach. I mean, at some point of time the velocities of both the trains and the bird change to zero. So, I think we would have to account for this sudden change of variables in our equations. But, the question is how.
 
Mathematics news on Phys.org
  • #2
'The answer'? You were asked two questions. There certainly will be an infinite number of trips (this is a perfectly valid thing in a model like this that has nothing to do with reality). But the time taken certainly isn't infinite. Indeed, the time taken can be deduced without even thinking about the bird.
 
  • #3
This goes to a series with an infinite number of terms, or trips, but finite value, or time taken.
 
  • #4
This remembers me of an anecdote about the famous mathematician John von Neumann:


When this problem was posed to John von Neumann, he immediately replied,
"150 miles."

"It is very strange," said the poser, "but nearly everyone tries to sum the
infinite series."

"What do you mean, strange?" asked Von Neumann. "That's how I did it!"
 
  • #5
How long does it take for the trains to touch each other?
 
  • #6
daniel_i_l said:
How long does it take for the trains to touch each other?

As long as v is not equal to 0, wouldn't that actually be "...for the trains to crash into each other"? Poor bird.
 
  • #7
Two trains initially separated by distance L are heading towards each other on the same track each with speed v
So they are closing on one another at speed 2v. It will take time L/2v (in whatever units are appropriate) for the two trains to "touch" (more correctly, crash). Since the bird flies at speed w, in that time it will have flown distance Lw/2v.
 

What does "The bird's got some guts" mean?

"The bird's got some guts" is an idiomatic expression that means someone or something has bravery or courage.

Why is "The bird's got some guts" often used to describe someone brave?

This expression comes from the idea that birds have a small body but a lot of courage when facing danger. So, when someone is described as "having guts like a bird", it means they may seem small or insignificant, but they possess a lot of bravery.

Is "The bird's got some guts" always used in a positive way?

Not necessarily. While it is often used to describe someone brave or courageous, it can also be used sarcastically or negatively to imply that someone is reckless or foolish.

Where did the phrase "The bird's got some guts" originate from?

The exact origin of this expression is unknown, but it is believed to have originated in the United States in the early 20th century. It may have been inspired by the behavior of birds in nature or by the bravery of birds in the face of danger.

Can "The bird's got some guts" be used to describe non-living things?

Yes, this expression can be used to describe non-living things as well. For example, it can be used to describe a machine or technology that is very bold or daring.

Similar threads

  • Introductory Physics Homework Help
Replies
20
Views
2K
  • Special and General Relativity
2
Replies
61
Views
3K
  • Special and General Relativity
Replies
21
Views
521
  • General Math
Replies
7
Views
429
  • Special and General Relativity
Replies
20
Views
1K
  • Special and General Relativity
Replies
25
Views
787
Replies
30
Views
2K
Replies
3
Views
637
Replies
14
Views
1K
Replies
2
Views
1K
Back
Top