Question

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?

Answer 1

Answer:

L= 12 light years

Explanation:

for length dilation we use the formula

$L=L_0\sqrt{1-\frac{v^2}{c^2} }$

now calculating Lo

Lo = 12.5×365×24×3600×3×10^8

= 1.183×10^17 m

now putting the values of v and Lo in the above equation we get

$L=1.183\times10^{17}\sqrt{1-\frac{0.28c^2}{c^2} }$

= 1.136×10^17 m

L=  $= \frac{1.136\times10^{17}}{365\times24\times3600\times3\times10^8}$m

so L= 12 light years