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170.

Problem 21.35 (RHK)

Observers S and stand at the origin of their respective frames, which are moving relative to each other with a speed 0.600 c. Each has a standard clock, which, as usual they set to zero when the two origins coincide. Observer S keeps the clock visually in sight. We have to find (a) the time the clock will record when the S clock records . (b) We have the find the time that observer S will actually read on the clock when the S clock reads .

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(a)

We will use the Lorentz transformations connecting the space-time co-ordinates of the same event observed by the observers in the frame S and that in the frame .

When the clock of S shows the co-ordinates of the origin of as measured by S will be

The speed of the frame , with respect to S is

The time shown on the clock of for this event will be

(b)

At the instant when the S-clock reads the signal communicating the reading on the clock of would have left it when it was at a distance l from S such that

The co-ordinates of this event in the S frame are

By Lorentz transformation we will calculate for this event. It is

 

The observer on S will read on the clock of when its clock shows .