I Video camera in a moving rocket

[Libor]

TL;DR Summary

how the recording video would look like?

Lets imagine that I will put the recording camera and ticking clock into a box and so that camera can record this clock all the time ticking. I will put then this box to the speed of 1/2 speed of the light, after a minute of mine I would stop this box and take the camera from it. As it was at that speed, the time for camera was slower, I will notice that camera recorded eg. 51 seconds of video, right? On this recorded video however was recorded 1minute of time. What would I see on that video please?

 

[Ibix]

Nearer 52 seconds than 51. Why do you think the video would have a minute of recording? It's just a fancy clock with a memory, so it'll behave the same as the clock it's filming.

 

[A.T.]

... camera can record this clock ...after a minute of mine... recorded 1 minute of time. ...

The camera is recording the clock, not you. Your time is irrelevant to what the camera records.

 

[anuttarasammyak]

Summary:: how the recording video would look like?
As it was at that speed, the time for camera was slower,

... and the time for clock in the box was slower also.

cf.
Say another camera in the box keep shooting your watch on the Earth through window. The recording show how much time of your watch? It is more than say 52 seconds ? If so it matches with relativity ? I myself do not have a simple way to answer.

 

[Ibix]

The recording show how much time of your watch?

Less, once you've accounted for the light travel time, since the camera cannot be co-located with your watch. I'd suggest that we should see where the OP takes this before adding complexity to the problem.

 

[A.T.]

Say another camera in the box keep shooting your watch on the Earth through window. The recording show how much time of your watch? It is more than say 52 seconds ? If so it matches with relativity ? I myself do not have a clear answer on it.

If the camera starts from your location and returns to you, then it will record the full minute on your clock between the meetings. But the rate of your clock as seen on the video might not be uniform.

 

[Libor]

Thank you for the answers