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

L= 12 light years

Step-by-step explanation:

for length dilation we use the formula

`L=L_0\sqrt{1-(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*10^(17)\sqrt{1-(0.28c^2)/(c^2) }`

= 1.136×10^17 m

L=
`= (1.136*10^(17))/(365*24*3600*3*10^8)`m

so L= 12 light years