Answer:
[tex]t=11.547\,s[/tex]
Explanation:
Given is the case of time dilation where the velocity of other spaceship is comparable to the velocity of light, i.e. relativistic velocity.
Given that:
velocity of the fast moving spaceship, [tex]v=(0.5\times c)\,\,m.s^{-1}[/tex]
where c is the velocity of light.
times according to the other spaceship, (relativistic time) [tex]t'=10\,s[/tex]
For time dilation we have the equation as:
[tex]t'=t \sqrt{1-\frac{v^2}{c^2} }[/tex]
[tex]\Rightarrow 10= t \sqrt{1-\frac{(0.5c)^2}{(c)^2} }[/tex]
[tex]t=11.547\,s[/tex]
