Answer:
The value is [tex]v = 2.999 *10^{8} \ m/s[/tex]
Explanation:
From the question we are told that
The time taken to travel to the planet from earth is [tex]t = 189 \ light-years[/tex]
The time to be spent on the ship is [tex]t_{s} = 12 \ years[/tex]
Generally speed can be obtained using the mathematical relation represented below
[tex]t_s = 2 * t * \sqrt{1 - \frac{v^2}{c^2 } }[/tex]
The 2 in the equation show that the trip is a round trip i.e going and coming back
=> [tex]12 = 2 * 189 * \sqrt{1 - \frac{v^2}{(3.0*10^{8})^2 } }[/tex]
=> [tex]v = 2.999 *10^{8} \ m/s[/tex]
