What is My Speed When Running on Top of a Moving Train?

[Sriram.S]

What speed am I traveling at when I am run at the top a moving train.(Assuming train is going at 10 km/hr and I am running at 2km/hr)

Sriram

 

[HallsofIvy]

Classical Physics:
If you are on a train going 10 km/hr, relative to the ground, and you are running at 2 km/hr relative to the train, toward the front of the train, then your speed relative to the ground is 10+2= 12 km/hr. If you are running toward the back of the train, your speed relative to the ground is 10-2= 8 km/hr.

Relativity:
If you are on a train going 10 km/hr, relative to the ground, and you are running at 2 km/hr relative to the train, toward the front of the train, then your speed relative to the ground is (10+2)/(1+ (10)(2)/c^2= (10+2)/(1+ 20/( 299,792,458)^2 which, even to 12 decimal place accuracy, the limit of my calculator, 12.000000000000 km/hr. Similarly, if you are running toward the back of the train, your speed is still 8 km/hr to with 12 decimal places.

Those speeds are simply to low for relativistic effects to be measurable.

 

[Rajini]

3.33 m/s [for stationary observer in ground]

 

[Fredrik]

even to 12 decimal place accuracy, the limit of my calculator, 12.000000000000 km/hr.

Microsoft PowerToy Calculator for Windows XP says 11.999999999999999258233295964254424402093624772443805600625656194569150201085437567008465314216160709462212415964961122075175062

By the way, that has to be the slowest runner ever, considering that normal walking speed is about 6 km/h.

 

[HallsofIvy]

Hey, YOU try running on top of a moving train!

 

[Tac-Tics]

You're at rest. You are always at rest relative to yourself.