4. If a second train heads through the station at 0.90c and appears to be 205.5 m long to
an observer standing in the station, what is the train's length at rest?

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:

[tex]L=L_0 \sqrt{1-\frac{v^2}{c^2}}[/tex]

where

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

[tex]L_0[/tex] 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

[tex]L=205.5 m[/tex] is the apparent length of the train

Solving for [tex]L_0[/tex], we find the length of the train at rest:

[tex]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[/tex]

#LearnwithBrainly

4. If a second train heads through the station at 0.90c and appears to be 205.5 m long to an observer standing in the station, what is the train's length at rest?

Respuesta :

Otras preguntas

4. If a second train heads through the station at 0.90c and appears to be 205.5 m long to
an observer standing in the station, what is the train's length at rest?