Special Relativity Astronaut Bill boards a spacesship and then zips past his bro

Question

Special Relativity

Astronaut Bill boards a spacesship and then zips past his brother, Will on earth at a relative speed of 0.600c. At the instant that Bill passes Will, both brothers start timers. (a) A short time later, Will measures that Bill has traveled 9.00 times 107 m beyond him and is passing a space station. What does Will timer read as Bill passes the space station? What does Bill timer read? Will starts to blink just as Bill flies past him again, and Bill measures that the blink takes 0.400s from beginning to end. According to Will, what is the duration of his blink?

Explanation / Answer

a)Willls timer reads 9*10^7/0.6c=1/2sec=0.5sec

Bills multiplying factor=sqrt(1-(v/c)^2)=sqrt(0.64)=0.8

distance for bill=0.8*9*10^7

time=0.8*1/2=0.4sec

b)According to bill duration of blink os given as =0.4se

duration as per will =0.4/0.8=0.5sec

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