Question

4. If a second train heads through the station at 0.90c and appears to be 205.5 m long to

Answer 1

The length of th train at rest is 471.4 m

Explanation:

Since the train is moving at a relativistic speed (=close to the speed of light), its length will appear contracted to an observer standing in the station, according to the equation:

$L=L_0 \sqrt{1-\frac{v^2}{c^2}}$

where

L is the apparent length of the train, measured by the observer

$L_0$ is the proper length of the train at rest

v is the speed of the train

c is the speed of light

In this problem, we have:

v = 0.90c is the speed of the train

$L=205.5 m$ is the apparent length of the train

Solving for $L_0$, we find the length of the train at rest:

$L_0 = \frac{L}{\sqrt{1-\frac{v^2}{c^2}}}=\frac{205.5}{\sqrt{1-\frac{(0.90c)^2}{c^2}}}=471.4 m$

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