Speed of Train B: Solving Physics Homework

AI Thread Summary
Two trains, A and B, are moving towards each other, with Train A traveling at 60 mph (approximately 26.82 m/s) and Train B being 45 meters long. It takes 0.5 seconds for the trains to completely pass each other, indicating that the total distance covered during this time is the sum of their lengths, which is 75 meters. To find Train B's speed, one can use the relative motion concept, treating Train A as stationary, leading to the conclusion that Train B must be traveling at 75 meters in 0.5 seconds, which equates to 150 m/s. The discussion also touches on calculating the relative velocity of Train B with respect to Train A. Understanding these principles clarifies the problem-solving process for physics homework involving relative motion.
Starsfall
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Homework Statement


Two trains run in opposite directions on parallel tracks. Train A is 30 meters long and runs east to west at 60 mph. Train B is 45 meters long and runs west to east. It takes 0.5 seconds for the trains to pass each other. How fast is train B travelling? What is the velocity of train B relative to train A?

Homework Equations

The Attempt at a Solution


I'm new to physics and lost with this problem. The first thing I did was convert mph to m/s. (60 miles/hour x 1609m/1m x 1 hour/3600s). I got 26.82 m/s but I don't know where to go from there?
 
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Welcome to PF!

I would first try drawing a diagram of the problem and see if you figure it out from there.

You could also assign the other train a velocity of x and think about velocity addition and how it may help you solve it.

Think about what it means for two trains to pass in 0.5 secs as in front to front and end to end.
 
I drew a sketch but that didn't seem to help much. I was thinking maybe 26.82 m/s x 0.5s = 13.02 m/s. I'm just really confused.
 
Starsfall said:
I drew a sketch but that didn't seem to help much. I was thinking maybe 26.82 m/s x 0.5s = 13.02 m/s. I'm just really confused.
It will be simplest to work in terms of relative motion. Consider an observer traveling at the rear of train A. The observer considers A to be stationary, so sees B traveling at the combined speed.
The observer sees the front of train B pass the front of train A, then half a second later the rear of train B pass herself. How far does it appear that train B has moved in that time?
 
haruspex said:
It will be simplest to work in terms of relative motion. Consider an observer traveling at the rear of train A. The observer considers A to be stationary, so sees B traveling at the combined speed.
The observer sees the front of train B pass the front of train A, then half a second later the rear of train B pass herself. How far does it appear that train B has moved in that time?

Would it be 75 meters?
 
r26h said:
Would it be 75 meters?
Yes.
 
r26h said:
Would it be 75 meters?
Can you now answer the second question, the relative velocity?
 

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