Answer:
Difference in Twin's Ages = 12.68 years
Explanation:
Using special theory of relativity's time dilation phenomenon, we first find the time that is passed on earth during Lou's trip.
t = t₀/[√(1 - v²/c²)]
where,
t = time measured by the person in relative motion = 1 year
t₀ = time measured by the person at rest = ?
v = speed of relative motion = 0.96 c
c = speed of light
Therefore,
1 year = t₀/[√(1 - 0.96² c²/c²)]
1 year = t₀/[√(1 - 0.9216)]
(1 year)(0.28 year) = t₀
t₀ = 0.28 year
Let,
y = Sue's age
x = Lou's age
so,
x - y = 13.4 years
but, after this trip Lou has aged 1 year, and on earth only 0.28 years passed so, Sue has aged only 0.28 years. Therefore,
x = x + 1
y = y + 0.28
Therefore,
(x + 1 year) - (y + 0.28 year) = 13.4 years
x - y = 13.4 years - 0.72 year
x - y = 12.68 years
<u>Difference in Twin's Ages = 12.68 years</u>
