Answer:
The value is [tex]v = 0.8587 c[/tex]
Explanation:
From the question we are told that
The time taken as seen by aliens [tex]T = 8.0 \ s[/tex]
The time taken as seen by attendant [tex]T_1 = 4.1 \ s[/tex]
Generally from the dilation of time equation we have that
[tex]T = \frac{T_1}{ \sqrt{ 1 - \frac{v^2}{c^2} } }[/tex]
Here c is the speed of light
v is the speed of the alien ship
=> [tex]8 = \frac{4.1}{ \sqrt{ 1 - \frac{v^2}{c^2} } }[/tex]
=> [tex]1 - \frac{v^2}{c^2} = [\frac{T_1}{T}] ^2[/tex]
=> [tex]1 - \frac{v^2}{c^2} = [\frac{4.1}{8}]^2[/tex]
=> [tex]v = 0.8587 c[/tex]
