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# there are two trains moving towards each other with a

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there are two trains moving towards each other with a [#permalink]  26 Jul 2003, 00:08
there are two trains moving towards each other with a constant velocity "v" . When the trains are a distance "D" appart a bird sitting on the engine of the 1st train starts to fly towards the second train that is coming from the front. The birds velocity is "B" that is B>v.
The bird touches the 2 nd trains and immidiately turns back to wards the first and keeps on doing this till both trains collide.
What is distance traveled by the bird
Hint : sum of infinite series...
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abhay pathania
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Re: Check this one out... [#permalink]  26 Jul 2003, 00:30
abhaypathania wrote:
there are two trains moving towards each other with a constant velocity "v" . When the trains are a distance "D" appart a bird sitting on the engine of the 1st train starts to fly towards the second train that is coming from the front. The birds velocity is "B" that is B>v.
The bird touches the 2 nd trains and immidiately turns back to wards the first and keeps on doing this till both trains collide.
What is distance traveled by the bird
Hint : sum of infinite series...

Is each train moving at "v" or are there approaching each other at "v" (e.g., each train moving at v/2)?

Remark to hint: you can solve this using sum of infinite series if you want to. But why, when you can solve this in your head without it?
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AkamaiBrah
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MBA, Anderson School of Management, UCLA, Class of 1993

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I assume that the ABSOLUTE speed of either train is V. Thus, their RELATIVE speed is 2v. The trains will collide in T=D/2V. All this time the bird can travel at its constant speed B. Its distance =BT=BD/2V.

If the RELATIVE speed of trains is V, then the answer is BD/V
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No matter what the relative speeds of train and bird, the total distance covered by the bird is 'D' ( taking the hint of infinite series - Geometric series )

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Brainless wrote:
No matter what the relative speeds of train and bird, the total distance covered by the bird is 'D' ( taking the hint of infinite series - Geometric series )

No, that is not correct. Stolyar has exactly the correct approach. The bird is flying at a constant speed. Hence, the distance covered is simply its speed multiplied by the total time it is in the air. (We are not worried about vectors here -- the distances all add up). The reason I ask for clarification re: the relative velocities of the trains, is that the trains approach each other with that relative velocity, hence, the time from the start of the problem until the trains crash is dependent upon which values we choice for the trains.
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AkamaiBrah
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MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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