# Distance traveled & velocity

## Homework Statement

Two trains, each having a speed of 25 km/h, are headed at each other on the same straight track. A bird that can fly 60 km/h flies off the front of one train when they are 57 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. (We have no idea why a bird would behave in this way.) What is the total distance the bird travels before the trains collide?

## The Attempt at a Solution

I am completely stumped on this one. I think I need to add the velocities since the trains are headed in the same direction but I am confused on determining when the bird will reach the other train. It also seems like there is an infinite number of returns that will get smaller and smaller and I am unclear If I need to apply some calculus to this problem.

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Why would the trains ever collide if they're traveling at the same speed? lol

They are headed at each other on the same track. Of course there displacement will be different since one will be negative.

Oh didn't read that, well I would do v=d/t to get 50=57/t, t=1.14 hours (total time the trains will move before colliding).
Then you have the time the bird will be traveling, the velocity it's traveling at, so you need to find the distance, so again v=d/t.. I think that helps :p

Oh didn't read that, well I would do v=d/t to get 50=57/t, t=1.14 hours (total time the trains will move before colliding).
Then you have the time the bird will be traveling, the velocity it's traveling at, so you need to find the distance, so again v=d/t.. I think that helps :p
Does this mean that all that is required is to calculate the distance the bird flies for 1.14 hours (68.4 km) ?

But I think it is a little more complicated then that. The bird keeps flying back from train to train until the trains finally meet.

gneill
Mentor
But I think it is a little more complicated then that. The bird keeps flying back from train to train until the trains finally meet.
What is the difference in total distance flown if the bird flies in a straight line at v m/s for one hour, or a crooked path at v m/s for one hour?

That's all you gotta do it doesn't matter if you go left, up, down, right, your total distance traveled is the same.