Answer:
0.992156741649c
Explanation:
[tex]\Delta t'[/tex] = Moving observer's period of the clock = 4 years
[tex]\Delta t[/tex] = Frame of the clock itself = 6 months = 0.5 years
c = Speed of light = [tex]3\times 10^8\ m/s[/tex]
v = Speed of the ship
Time dilation is given by
[tex]\Delta t'=\dfrac{\Delta t}{\sqrt{1-\dfrac{v^2}{c^2}}}\\\Rightarrow 4=\dfrac{0.5}{\sqrt{1-\dfrac{v^2}{c^2}}}\\\Rightarrow \dfrac{0.5}{4}=\sqrt{1-\dfrac{v^2}{c^2}}\\\Rightarrow 0.125=\sqrt{1-\dfrac{v^2}{c^2}}\\\Rightarrow 0.015625=1-\dfrac{v^2}{c^2}\\\Rightarrow 0.984375=\dfrac{v^2}{c^2}\\\Rightarrow v^2=0.984375c^2\\\Rightarrow v=\sqrt{0.984375c^2}\\\Rightarrow v=0.992156741649c[/tex]
The speed of the ship should be 0.992156741649c
