2 Train aight line at constant velocity to station B, 300 km away. a. If the tra

Question

2 Train aight line at constant velocity to station B, 300 km away. a. If the train is traveling at 100 kph do the passengers and crew observe the distance from A to B to be substantially different from 300 km? b. Repeat part (a) for a train traveling at 2x 105 km per second. c. If the train is traveling at 100 kph and a rocket ship, traveling in the same direction as the train but at 0.9c, observes its journey, how far will the rocket ship see the train travel between stations? d. How long will the train journey take according to the rocket ship? (Hint: does the train velocity really matter in this case?)

Explanation / Answer

a. v = 100 km / h = 100 x 1000 m / 3600s

v =27.8 m/s

Y = 1 / sqrt(1 - (v/c)^2)

v/c < < < 1

so Y = 1

hence distance will be same.

(B) now v = (2 x 10^5) x 10^3 m /s

= 2 x 10^8 m/s

Y = 1 / sqrt[ 1 - (v/c)^2] = 1.34

distance observed = 300/Y = 223.6 km ......Ans

(C) Y = 1 / sqrt(1 - 0.9^2) = 2.29

observed distance = 300 / Y = 130.8 km

(D) t = (300 x 10^3/ 27.8)/2.29

t = 4712.4 sec

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