Question

A passanger travels on a train which is moving at constant speed 0.75c with respect a station. A worker in the station opens his mouth and then closes it. If the passanger observs that the worker kept his mouth open for 8.0 seconds ¿how long does the worker think he open his mouth?

Answer 1

Here we have to calculate the proper time.

We now the equation for time dilation

Where v is speed of the observer, c is speed of light, is dilated time, is proper time.

Given, ,

Therefore,

Or,

or,

Hence, the worker opened his mouth for 5.3 seconds in his own reference frame.