Why is the distance traveled by the bird towards the wall incorrect?

[chaoseverlasting]

Homework Statement

A bird, 720 km away from a train flies towards it at a speed of 120km/h. As soon as it reaches the train, it turns back towards the wall (starting position). The train travels at a speed of 15m/s towards the starting position of the bird. How much distance towards the wall will the bird cover before the train reaches it.

The Attempt at a Solution

15m/s= 54km/h

Thus the train takes 720/54=13.33 hours to reach the wall.

The relative velocity of the bird wrt train when traveling towards it is 54+120=174km/h

The relative velocity when traveling away from the train is 120-54=66km/h

Ratios of velocities (towards:away)=29:11

Thus the ratio of time taken in traveling towards the train to away from the train =11:29

Thus, the bird spent a total of $$\frac{29}{29+11}\times 13.33$$ hours traveling away from the train.

The velocity of the bird traveling away from the train is 120km/h

Thus, the distance traveled by the bird away from the train is $$13.33\times \frac{29}{40} \times 120=1160 km$$

Which is the wrong answer. The solution is 800 km. Why?

 

[AC130Nav]

Homework Statement

A bird, 720 km away from a train flies towards it at a speed of 120km/h. As soon as it reaches the train, it turns back towards the wall (starting position). The train travels at a speed of 15m/s towards the starting position of the bird. How much distance towards the wall will the bird cover before the train reaches it.

I don't see where you computed at what point the (extremely fast) bird and the train meet. Relative velocities are unimportant. The 800 km seems to be how far beyond the wall the bird will get, since it's faster than the train.

 

[chaoseverlasting]

The bird flies towards the train and as soon as it meets the train, it turns back and flies at the wall. 800 km is the total distance covered by the bird while its flying away from the train. For example, the distance covered in the first run is $$\frac{720}{120+54}\times 120$$ km (towards the train).

 

[Bartek]

Thus the ratio of time taken in traveling towards the train to away from the train =11:29

Thus, the bird spent a total of $$\frac{29}{29+11}\times 13.33$$ hours traveling away from the train.

It is bad reasoning. Imagine that a bird has the same velocity as the train. Relative velocity toward the train is 240km/h, toward away - 0km/h! But in this case time to fly toward away has to be infinity. It is clear that it is not true - bird back starting point together with the train!

Now imagine that bird fly ONLY ONCE toward the train and back. What is the ratio of time to fly toward train to toward back? Remember that there is no matter where bird meet the train.

regards

 

[Niles]

Isn't the correct answer 607 km past the wall, and not 800?

 

[Bartek]

Isn't the correct answer 607 km past the wall, and not 800?

No, 800 is right.

regards

 

[chaoseverlasting]

Ok. I see where I've made the mistake. The velocity towards the wall is 120 km/h and towards the train is 174km/h.

Ratio of time taken flying towards the train to away from the train is 120:174 (=20:29)

Total time spent flying away is $$\frac{13.33\times 29}{49}$$

Speed of the bird is 120km/h

This gives a distance of 946.77 ...

 

[Bartek]

The velocity towards the wall is 120 km/h and towards the train is 174km/h.

Ratio of time taken flying towards the train to away from the train is 120:174 (=20:29)

Forget about the train! . There is no train - train sets only the rendezvous points.

Your problem looks like: "There is a bird flying from A to B and then backward. How many time it is flying back?".

Answer is simply: half of the time, isn't it?

Then the bird flying again from A to C and backward... the same. A -> D -> A? The same. In all cases half of the time it is going toward point of meeting and half of the time backward. No matter where that points are.

So, no matter train speed and relative speed. Train sets only B, C, D... turning points.

Train is nessecary only to calculate total time of flying. Half of that time bird is going toward "away from train". And you know velocity .

regards
Bartek
of course, the speed of the bird must be greater than the speed of the train. In order to fly earlier than the train to the starting point.

BTW... bird flying for over 13 hours with speed 120 km/h. wow!

 

[Rajini]

Is your question is well written? i suspect it is not. (Please check your question again)
What i understand is:
Train and bird going towards each other. After 4.138 h (=720/(120+54)) train and bird will meet. So bird will cross 496.552 km (=120 km/h X 4.138 h). So for the bird to go back to starting position it will have to travel another 496.552 km.
That means the total distance traveled by bird will be 2 X 496.552 = 993.103 km.

 

[Bartek]

So for the bird to go back to starting position it will have to travel another 496.552 km.
That means the total distance traveled by bird will be 2 X 496.552 = 993.103 km.

I understand that bird flying toward the train, then back to "wall" then again fly to train and back to the train and back and again and again until the train reaches "the wall".

If I'm right - total distance is 1600km and distance toward starting point is 800km.

 

[Rajini]

I understand that bird flying toward the train, then back to "wall" then again fly to train and back to the train and back and again and again until the train reaches "the wall".

If I'm right total distance is 1600km and distance toward starting point is 800km.

I don't know! In his question he did not tell anything about going back again and again..From his question i understand that the bird travel from starting position to train and then back to starting position. I gues we have to wait for his reply.

 

[Bartek]

In his question he did not tell anything about going back again and again..

You are right. So I understand sentence "distance towards the wall will the bird cover before the train reaches it". It make no sense (for me) if the bird flying only once. There is no matter how much time spent the bird on ending point before train reaches it.

If you are right, chaoseverlasting just have two homework in one

regards
Bartek

 

[Rajini]

Hello Bartek,
you notice the original question carefully. Moreover, in return journey for the bird, no need to consider the train's velocity. That why i asked him to write the question properly (scroll above). So I believe your solutions should be correct. I think he may have even more than two homework in one.

 

[Bartek]

That why i asked him to write the question properly (scroll above).

Lets wait what chaoseverlasting say . He wrote right answer:

Which is the wrong answer. The solution is 800 km. Why?

I think it is from book.

regards
Bartek

 

[Niles]

I don't know! In his question he did not tell anything about going back again and again..From his question i understand that the bird travel from starting position to train and then back to starting position. I gues we have to wait for his reply.

I agree with you. I thought the bird started from the wall, flew to the train, and then towards the wall and beyond it. The task is to find the distance passed from the wall and beyond (I got 607 km). But I think Bartek has understood the question correctly (his solution is also 800 km, just as in the book).

But I think all of us agree that it is a very impressive bird flying 120 km!

 

[Rajini]

Is this speed is really high for a bird ?..Anyway this bird is amazing.

 

[chaoseverlasting]

Thank you bartek! It is from a book. I've been solving similar questions, and missed the point. A result of less thinking and blind application. :) Kudos!