Answer:
option c) 0.88c is the correct answer
Explanation:
using the Lorrentz equation we have
[tex]t=\frac{d}{v}\sqrt{1-(\frac{v}{c})^2}[/tex]
where,
t = time taken to cover the distance
d = Distance
v = velocity
c = speed of light
given
d = 15 light years
Now,
[tex]8years=\frac{15years\times c}{v}\sqrt{1-(\frac{v}{c})^2}[/tex]
or
[tex](\frac{v}{c})^2\times (\frac{8}{15})^2=1-(\frac{v}{c})^2[/tex]
or
[tex](\frac{v}{c})^2\times 0.284=1-(\frac{v}{c})^2[/tex]
or
[tex](\frac{v}{c})^2\times 0.284 + (\frac{v}{c})^2 =1[/tex]
or
[tex](1.284\times \frac{v}{c})^2 =1[/tex]
or
[tex] (\frac{v}{c}) =\sqrt{\frac{1}{0.284}}[/tex]
or
[tex]v=0.88c[/tex]
