# A runner inside a train, and it stops

This concerns a debate I'm having with two friends of mine, hope someone here can help.

You have a train travelling at 100km/h. Inside the train there is a car travelling at 100km/h. Inside the car is a jogger running at 20km/h.

Suddenly the train and car stop and the jogger is thrown forward out of the train and car. At what speed relative to an outside observer?

100? 200? 220?

(We are Computer Scientists hence our lack of understanding :) )

## Answers and Replies

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Each aspect is a different system. The train itself and then the car. Inside the car the runner is going at 20km/hr. Inside the train the runner is going 100km/hr regardless of how fast he's running because the car is a lone system. Since the train is traveling at 100km/hr everythig inside the train is traveling at the same speed with repesct to the observer outside. So your answer is 100km/hr.

(If the observer was in the train it would be 100km/hr and if the observer was in the car with the runner it would only be 20km/hr. Everrything depends on the system the observer is viewing.)

BTW, this question is General Relativity. You could repost this in that section if you would like more responses.

DaveC426913
Gold Member
Inside the train the runner is going 100km/hr regardless of how fast he's running because the car is a lone system.
Please reread. The jogger is INSIDE the car.

The jogger will exit the train at 220km/h as observed from the ground.

arildno
Homework Helper
Gold Member
Dearly Missed
BTW, this question is General Relativity. You could repost this in that section if you would like more responses.
Eehh??

HallsofIvy
Homework Helper
this certainly involves "relativity" but not "Einsteinian" relativity, either "special" or "general". The speeds involved just aren't high enough for such effects to be measurable. This is purely "Gallilean relativity".

I am assuming that the car is moving toward the front of the train and the person is running toward the front of the car.
To a person sitting inside the car the man is running at 20 kmph. To a person standing inside the train the car is travelling at 100 kmph and the runner an additional 20 kmph: 120 kmph. To a person standing outside the train the train is doing 100 kmph the car an additional 100 kmph and the runner yet another 20 kmph: the runner is doing 220 kmph relative the the ground.

(A relativistic calculation would give that the person is running, relative to an observer in the train at (100+ 20)/(1+ (100)(20)/c2)= 119.99999999999733333333333339259 kmph. and, relative to a person on the ground, 219.99999999996800000000000497769 kmph. Of course, with the speeds given to 2 and 3 significant figures, that accuracy is meaningless. those are 120 and 220 kmph rounded to reasonable accuracy.)

You did not state at what speed relative to the train/car/person/other reference frame the outside observer is traveling at. Although for this reason, your question is slightly ambiguous, but I think we all know what you mean.

The problem is probably better stated backwards. The person is running at 20km/h relative to the car which is traveling at 100km/h relative to the train, which is traveling at 100km/h relative to reference frame A. I assume they are all traveling in the same direction so the persons speed is simply the sum of the three speeds in classical mechanics. This is 220km/h in reference frame A. When the dude is flung out, assuming no friction has slowed him down, he will still be gonig at 220km/h.

Things are slightly different in special rel where velocities are not simply summed. A good explanation of this is given by wikipedia but needless to say, at these velocities, it is basically 220km/h.

Looks like someone beat me to it. In that case, what he said.

So I was wrong. :)

Thanks a lot for the informative replies.

Please reread. The jogger is INSIDE the car.

Exactly! Therefore he can only travel as fast as the car is traveling and the car (INSIDE the train) can only travel as fast as the train is traveling.

Danger
Gold Member
Exactly! Therefore he can only travel as fast as the car is traveling and the car (INSIDE the train) can only travel as fast as the train is traveling.

Your logic eludes me.

DaveC426913
Gold Member
Please reread. The jogger is INSIDE the car.

Exactly! Therefore he can only travel as fast as the car is traveling and the car (INSIDE the train) can only travel as fast as the train is traveling.
Why? The automobile is moving at 100km/h with respect to the train (obviously, it is on a very short raceway). So the speed of the automobile from the vantage point of the ground is the train's speed plus the automobile's speed within the train, for a total of 200km/h.

Same can be done between the automobile and the jogger. You sum the three velocities.

The train and car do not have to suddenly stop. As long as they are all in motion, the runner IS traveling 220km/h relative to the outside observer. This is just an exercise in frames of reference.

To the outside observer the train is traveling +100km/h, the car is traveling +200km/h, and the runner is traveling +220km/h.

To an observer sitting in the train, the outside observer is traveling -100km/h, the car is traveling +100km/h, and the runner is traveling +120km/h.

To an observer sitting in the car, the outside observer is traveling -200km/h, the train is traveling -100km/h, and the runner is traveling +20km/h.

To the runner, the outside observer is traveling -220km/h, the train is traveling -120km/h, and the car is traveling -20km/h.

Danger
Gold Member
I'm still trying to figure out how the hell somebody can run inside a car. I've done a few things in a car, that didn't involve running, and felt cramped.

DaveC426913
Gold Member
I'm still trying to figure out how the hell somebody can run inside a car. I've done a few things in a car, that didn't involve running, and felt cramped.
Yes. I thought it wasn't the best setup for the thought experiment, but it will do.

My only concern was that perhaps the jogger-versus-car was what might have been confusing GetPhysical.

Danger
Gold Member
perhaps the jogger-versus-car was what might have been confusing GetPhysical.
Possible, I suppose. I hadn't thought of that.