In the question 1, is your approximate speed relative to the Sun as you walk down the aisle of the train slightly more or very much more? Question 1 If you walk at 1 km/h down the aisle of a train that moves at 60 km/h, what is your speed relative to the ground?
Solution Step 1 of 3 In question 1, Here since the speeds are very less compared to speed of light, we can use normal velocity vector addition; The speed of the person moving on the aisle of train with respect to ground (assuming the person is moving towards front end of train) vpersonground= vtrainground v persontrain Where v is the speed of person relative to ground personground v traingrounds the speed of train relative to ground v persontrains the speed of person relative to train Using v trainground0 km/h and v persontrain1 km/h in above equation, vpersonground= 60 km/h + 1 km/h v = 61 km/h personground Therefore, the speed of person moving on aisle of train relative to ground is 61 km/h. Step 2 of 3 To calculate the speed of the person relative to sun (For the same person moving on aisle of train) As here the speed of earth relative to sun is very high, we have to solve this in the relativistic limit. This can be calculated using Einstein's velocity addition theorem, The speed of the object relative to rest observer is, 1 u = v+u 1 ……………….1 1+ v2 c Where c is the speed of light.