If you run 10mph inside of a train that is moving 100mph, are you moving 110mph or 100mph?
In: Physics
Neither, cuz I’m measuring from a car on the parallel highway, going 50 mph over the ground, the other way.
From my pov, you are going 160 mph toward me. Pretty fly for a human
Relative to a stationary observer on the ground:
0 – (100 + 10) = -110
You’re travelling 110 mph away from the observer.
Relative to train, running from back to front:
100 – (100 +10) = 10
You’re travelling 10 mph towards the front.
Relative to train, running from front to back:
100 – 10 = 90
You’re travelling 10mph away from the front.
Relative to what? To the train you’re running 10mph, to the ground you’re running 110mph, to space in which the Earth spins you’re running 1,110mph (well, assuming the train is going east; if it’s headed west you’re running 890mph).
Look at this Einstein over here! No, seriously, this is what bugged Einstein.
To an observer in a reference frame where the train is going at a 100mph you will appear to be going 110 mph. To an observer on the train you will appear to be going 10 mph. To an observer in a car going 50 mph in the same direction you will look like you’re going 60 mph. Conversely, you will see the person standing next to the tracks zooming back at 110 mph and other passengers in the train going back at 10 mph.
This is Galilean (or classical) relativity. Perceived speed is 100% relative to the observer’s reference frame.
But then Einstein looked at [Maxwell’s equations ](https://en.wikipedia.org/wiki/Maxwell%27s_equations)and realized that for all those observers, *the speed of light is constant.* So if you are a photon running at the speed of light on that train, you are going at the same speed for all those observers! To have this make any sense you need to accept the fact that as you accelerate time dilates and space contracts, but that’s above my ELI5 abilities.
But, as a result of this, if you run 10 miles per hour on the train, the “stationary” observer will see you as going VERY slightly less than 110 mph.
Everyone here is assuming OP is running from back to front!
If so, 110MPH over the ground.
If running from front to back, 90MPH over the ground!
I think this has been answered , but with the assumption that you are running in the same direction that the train is moving. If you ran towards the rear (opposite direction from the train) you would be moving 90 mph in the same direction as the train.
It’s also important to realize that speed depends on what you compare. The train is moving 100 mph relative to the ground, but the earth is rotating and is also orbiting the sun. So you could be moving a thousand miles per hour compared to the center of the earth, or millions of miles per hour compared to the sun.
110 relative to the ground. Or 90, if you run the other way.
In either case, Earth is moving through space at about 230 miles per second.
Don’t forget to factor in that the earth itself is moving at 67,000 miles per hour through space
You are moving 10 miles on hour. By the 110 mph analogy, one could reasonably argue that you are moving at roughly 67,110 mph due to the movement of the Earth. As previously posted, it is always relative to a stationary object. Sadly, there is no such thing as stationary objects in this universe. Again, it all comes down to spatial relativity.
It depends on the reference frame. You are moving 10mph relative to the train, 110mph relative to a static point outside the train.
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