Answer:
The speed is 0.97 c.
Explanation:
Given that,
Dilated time t'= 50.0 years
Rest time t = 13.0 years
We need to calculate the speed
Using formula of time dilation
[tex]t'=\dfrac{t}{\sqrt{1-\dfrac{v^2}{c^2}}}[/tex]
Where, t' = change in time
t = rest time
v = velocity
c = speed of light
Put the value into the formula
[tex]50.0=\dfrac{13.0}{\sqrt{1-\dfrac{v^2}{(3\times10^{8})^2}}}[/tex]
[tex]v^2=\dfrac{(13)^2\times(c)^2-(c)^2\times50^2}{50^2}[/tex]
[tex]v^2= 0.9324c^2[/tex]
[tex]v=0.97c[/tex]
Hence, The speed is 0.97 c.
