Train and Bird Collision: Calculating Trips and Distance

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Two trains traveling towards each other at 34 km/h will collide after 1.5 hours, covering a distance of 102 km. During this time, the bird flying at 58 km/h continuously travels back and forth between the trains. The total distance the bird travels can be calculated as 87 km, which is the product of its speed and the time until the trains collide. The bird can make an infinite number of trips back and forth between the trains, as it turns around instantly after reaching each train. Thus, the bird's journey is limited only by the time until the trains crash.
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Two trains, each having a speed of 34 km/h, are headed at each other on the same track. A bird that can fly 58 km/h flies off the front of one train when they are 102 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.

(a) How many trips can the bird make from one train to the other before they crash?

(b) what is the total distance the bird travels?


*If possible show solution
 
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Rock00 said:
Two trains, each having a speed of 34 km/h, are headed at each other on the same track. A bird that can fly 58 km/h flies off the front of one train when they are 102 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.

(a) How many trips can the bird make from one train to the other before they crash?

(b) what is the total distance the bird travels?


*If possible show solution
Think of the problem in the frame of reference of one of the trains. Think of the bird flying continuously at 58 km/hr until the separation = 0. How long does that take? How far does the bird fly? The more difficult part is (a). If it takes no time to turn around and accelerate back up to 58 km/hr, I don't think there is a limit to the number of trips.

AM
 
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