Part A Astronaut Sarah leaves Earth in a spaceship at a speed of 0.280 c relativ

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Question

Part A

Astronaut Sarah leaves Earth in a spaceship at a speed of 0.280c relative to Earth. Sarah's destination is a star system 12.5 light-years away (one light-year is the distance light travels in one year). According to Sarah, how far did she travel during the trip?

11.5 light-years 13.0 light-years 12.5 light-years 12.0 light-years 11.0 light-years

Explanation / Answer

For length dilation,

L = Lo(1- v^2/c^2)^(1/2)

Now, Lo = 12.5*365*24*3600*3*10^8 = 1.183*10^17 m

So, L = 1.183*10^17*(1- 0.28^2)^(1/2) = 1.136*!0^17 m

So, L = 1.136*10^17/(365*24*3600*3*10^8) = 12 light years <--------answer

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Part A Astronaut Sarah leaves Earth in a spaceship at a speed of 0.280 c relativ

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