Question

An astronaut leaves Earth in a spaceship at a speed of 0.96 c relative to an observer on Earth. The astronaut's destination is a star system 14.4 light-years away (one light-year is the distance light travels in one year.) According to the astronaut, how long does the trip take?

Answer 1

Answer:

t=4.2 years

Explanation:

velocity v= 0.96c

destination star distance = 14.4 light year

According to the theory of relativity length contraction

$l= \frac{l_0}{\sqrt{1-\frac{v^2}{c^2}}}$

$l_0= l{\sqrt{1-\frac{v^2}{c^2}}}$

putting values we get

$l_0= 14.4{\sqrt{1-\frac{(0.96c)^2}{c^2}}}$

$l_0= 4.032 light years$

now distance the trip covers

D= vt

$4.032\times c= 0.96c\times t$

$t= \frac{4.032c}{0.96c}$

t= 4.2 years

so the trip will take 4.2 years