speed of a train relative to a passenger

Question

2 trains pass each other. One is going east at 70 mph; the other is travelling west at 50 mph. A passenger on the eastbound train walks toward the back of the train at 5 km per hour. Relative to the passenger, what is the speed of the westbound train?

Answer 1

It's always best to draw these problems, or any other physics problems out in a little diagram or sketch. I haven't figured out how to do this on WyzAnt yet, but the day will come. Meanwhile,

 

I prefer to always set up a fixed unaccelerated reference frame for this type of problem. It saves confusion.

 

In this case, I'll imagine I'm an observer standing beside the tracks, watching all the exciting action.

 

I see the eastbound train passing me at 70 mph.

 

I see the passenger on the eastbound train walking toward the back of the train at a velocity of 5 kph. That's equivalent to 3 mph (slightly rounded). So I see the passenger carried to the east at 70 mph by the train but carried back towards the west (the rear of the eastbound train) at 3 mph, against the motion of the train. So I see the passenger moving toward the east at a total of 70-3 = 67 mph.

 

The passenger is moving east at 67 mph and the westbound train is moving west at 50 mph, so I see the westbound train is moving with respect to the passenger (her reference frame, that is) at 67 + 50 mph = 117mph. Which is what the passenger sees.