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Thank you in advance.

Problem : A command centre gets message that a meteor has just passed one of its outposts located 100 light seconds away, the meteor is traveling at 1/4 light speed and headed towards the command centre. How long does the command centre have for evasive action (radio messages travel at light speed)

__Ans (in textbook)__: The message takes 100 light seconds to reach the command centre. As the metero is traveling at 1/4 light speed, it will take a total of 400 light seconds. Hence time available for evasive action = 300 light seconds.

__Alternate calculation__: Since message takes 100 light seconds to reach earth, distance from outpost to centre = 3e8 / 100 = 3e10 m

For the meteor this distance appears as 3e10*sqrt(1-0.25^2) = 2.9e10 m due to length contraction.

hence time for meteor to reach = 2.9e10 / 0.25*3e8 = 387 light secs

Therefore time for evasion = 287 light secs