A hypothetical train moving with a speed of 0.6 c passes by the platform of a small station without being slowed down. The observes on the platform note that the length of the train is just equal to the length of the platform which is 200 m . (a) Find the rest length of the train (b) Find the length of the platform as measured by the obsevers in the train .

Explanation

(a) The length L' of the train at a speed 0.6c is 200m. If the rest length is L,
`L' = L (sqrt 1 - V^(2) / c^(2))`
L (sqrt 1 - V^(2) / c^(2)) = 200 m / (sqrt 1- (0.6)^(2))`
= 250 m. (b) The rest lenth of the platform is 200m. For the observes in the train, the platform is moving at a speed of 0.6c. The length as measured by the observers in the train is , therefore ,
` L' = 200m (sqrt 1- (0.6)^(2))= 160m`.