Answer:
v = 0.99 c = 2.99 x 10⁸ m/s
Explanation:
From the special theory of relativity:
[tex]t = \frac{t_o}{\sqrt{1-\frac{v^2}{c^2} } }\\[/tex]
where,
v = speed of travel = ?
c = speed of light = 3 x 10⁸ m/s
t = time measured on earth = 90 years
t₀ = time measured in moving frame = 6 months = 0.5 year
Therefore,
[tex]90\ yr = \frac{0.5\ yr}{\sqrt{1-\frac{v^2}{c^2} } } \\\\\\\sqrt{1-\frac{v^2}{c^2}} = \frac{0.5\ yr}{90\ yr}\\ 1-\frac{v^2}{c^2} = 0.00003086\\\frac{v^2}{c^2} = 1-0.00003086\\[/tex]
v = 0.99 c = 2.99 x 10⁸ m/s
