Bird & Trains: Calculating Distance & Speed

[zaske.014]

using instantaneous vs. velocity/speed

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 traveled by the bird?

this is the image that i make...

http://www.soulroph.somee.com/trains[/URL] and bird.bmp[/PLAIN]

please help me to solve this kind of problem...

Thanks...

 

[Kurdt]

It is the policy of this forum that you make some attempt at the problem yourself before anyone can help. Please show what you've attempted so far.

 

[m2003]

A) The bird can make an infinite number of trips between the trains before they crash. This is because the trains are constantly moving towards each other, so the distance between them will always be decreasing. Therefore, the bird will never reach the trains and can continue flying back and forth indefinitely.

B) The total distance traveled by the bird can be calculated by considering each trip as a round trip from one train to the other and back. The distance between the trains when the bird starts its first trip is 102 km. The bird flies at a speed of 58 km/h, so it takes 102/58 = 1.76 hours to reach the other train. In this time, the trains have also moved 34*1.76 = 59.84 km closer to each other. This means that the bird has to fly a total distance of 59.84 km to reach the other train. On the return trip, the distance between the trains is now 102 - 59.84 = 42.16 km. The bird flies at 58 km/h, so it takes 42.16/58 = 0.73 hours to reach the first train. In this time, the trains have moved 34*0.73 = 24.82 km closer to each other. Therefore, the bird has to fly a total distance of 24.82 km to reach the first train.

This cycle continues for each trip, with the distance between the trains decreasing by 34 km for each round trip. So, the total distance traveled by the bird can be calculated as:
Distance traveled = 59.84 + 24.82 + (59.84-34) + (24.82-34) + (59.84-2*34) + (24.82-2*34) + ...
= 59.84 + 24.82 + 25.84 + 6.82 + 25.84 - 9.18 + 25.84 - 15.18 + ...
= 59.84 + 24.82 + 25.84 + 6.82 + 25.84 - 9.18 + 25.84 - 15.18 + ...
= 59.84 + 24.82 + 25.84 + 6.82 + 25.84 - 9.18 + 25.84 - 15.18