Imagine that a relativistic train travels past your lecture room at a speed of 0

Question

Imagine that a relativistic train travels past your lecture room at a speed of 0.883 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 69.1 m. What would be the length of the train in the frame of the lecture room if you measured it? (in m) A: 1.33 times 10^1 B: 1.66 times 10^1 C: 2.08 times 10^1 D: 2.59 times 10^1 E: 3.24 times 10^1 F: 4.05 times 10^1 G: 5.07 times 10^1 H: 6.33 times 10^1 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: 5.07 times 10^1 B: 7.35 times 10^1 C: 1.07 times 10^2 D: 1.54 times 10^2 E: 2.24 times 10^2 F: 3.25 times 10^2 G: 4.71 times 10^2 H: 6.83 times 10^2

Explanation / Answer

formula for length contraction is

L = Lo sqrt 1- v^2/c^2

=69.1 sqrt ( 1- (0.883c/c)^2

=3.24 * 10^1 m

option (E) is correct answer

from the time dilation equation

' = /(1 -v2/c2)

= 50 min/ sqrt ( 1- (0.883c/c)^2

= 106.52min

= 1.07 * 10^1 min

option (C) is correct answer

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