Answer:
The velocity as a fraction of c is 0.986 c m/s
Solution:
As per the question:
Time measured by the astronaut, t = 15 yrs
Time measured in the frame of mission control, t' = 130 yrs
Now,
Using the formula of time dilation:
[tex]t' = \frac{t}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}[/tex]
Substituting appropriate values in the above eqn:
[tex]130 = \frac{15}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}[/tex]
[tex]\sqrt{1 - \frac{v^{2}}{c^{2}}}= \frac{15}{130}[/tex]
Squaring both the sides we get:
[tex]1 - \frac{v^{2}}{c^{2}}= (\frac{15}{130})^{2}[/tex]
[tex]\frac{v^{2}}{c^{2}} = 1 - (\frac{15}{130})^{2}[/tex]
v = 0.986 c m/s
