Question

Imagine that a relativistic train travels past your lecture room at a speed of 0.954 c. The passengers of the train claim that when they measure the length of the train using standard meter bars found on the train, the length comes out to be 73.6 m. What would be the length of the train in the frame of the lecture room if you measured it?
(in m)

A: 1.64

B: 2.37

C: 3.44

D: 4.99

E: 7.24

F: 1.05×101

G: 1.52×101

H: 2.21×101

How long would a regular 50 minute long class in the lecture room last for the passengers of the train if they measured it while sitting on the train?
(in min)

A: 2.60×101

B: 3.77×101

C: 5.47×101

D: 7.93×101

E: 1.15×102

F: 1.67×102

G: 2.42×102

H: 3.51×102

Answer 1

$L=\frac{L_{0}}{\gamma(v)}=L_{0}\sqrt{1-v^{2}/c^{2}}$

L₀ is the proper length (the length of the object in its rest frame),

L is the length observed by an observer in relative motion with respect to the object,

v is the relative velocity between the observer and the moving object,

c is the speed of light,

L = 73.6*sqrt(1-0.954^2) = 22.1 m = 2.21*10^1

$\Delta t'={\frac {\Delta t}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}$

t' = 50 / sqrt(1-0.954^2) = 167 min = 1.67*10^2