Relativity Problem: Time Dilation and Light Signals in a Rocket Ship

[Arijit Dutta]

Homework Statement

A rocket ship leaves Earth at a speed of 3c/5. When a clock on the rocket says 1 hour has elapsed, the rocket ship sends a light signal back to earth.

(a) According to Earth clocks, when was the signal sent?
(b) According to Earth clocks, how long after the rocket left did the signal arrive back on earth?
(c) According to the rocket observer, how long after the rocket left did the signal arrive back on earth?

Homework Equations

∆t' = ∆t/ℽ

The Attempt at a Solution

(a)Applying the time dilation eqn. we find that the ans is 1hr 15 min.

(b) Distance traveled by the rocket as seen by the observer on earth= (3c/5)(5/4hr)= 3c/4 hr
Time taken by light to travel this distance = 3/4 hr.
so, total time= 3/4+3/4 = 2hrs.

(c) Applying a similar reasoning wrt rocket we find total time = 1+3/5 = 8/5 hrs.

The last ans seems erroneous. Please correct my reasoning if I'm wrong.

 

[nilesh_pat]

Also,I'm not sure how to approach the first part of the question. Any help would be greatly appreciated. Thanks.