Question

A futuristic train rushes past you at an incredible, relativistic speed such that it appears to only be 80% as long as you know it to be. At what speed is that train traveling from the point of view of your reference frame

Answer 1

Answer:

v = 0.6c = 1.8 x 10⁸ m/s

Explanation:

From Einstein's theory of relativity, we know that the length of an object contracts while traveling at a speed relative to speed of light. The contraction is according to following equation:

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

where,

L = Relative Length

L₀ = Rest Length

According to given:

L = 0.8 L₀

c = speed of light = 3 x 10⁸ m/s

v = relative speed of train = ?

Therefore,

$0.8L_{0} = L_{0}\sqrt{1 - \frac{v^2}{c^2} } \\\\0.8 = \sqrt{1 - \frac{v^2}{c^2} }$

squaring on both sides:

$0.64 = 1-\frac{v^2}{c^2}\\\\\frac{v^2}{c^2} = 1-0.64 \\v^2= 0.36c^2$

taking square root on both sides:

v = 0.6c = 1.8 x 10⁸ m/s