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Sagot :
Answer:
Explanation:
This is a problem based on time dilation , a theory given by Albert Einstein .
The formula of time dilation is as follows .
t₁ = [tex]\frac{t}{\sqrt{1-\frac{v^2}{c^2} } }[/tex]
t is time measured on the earth and t₁ is time measured by man on ship .
A ) Given t = 20 years , t₁ = ? v = .4c
[tex]\frac{20}{\sqrt{1-\frac{.16c^2}{c^2} } }[/tex]
=1.09 x 20
t₁= 21.82 years
B ) Given t = 5 years , t₁ = ? v = .2c
[tex]\frac{5}{\sqrt{1-\frac{.04c^2}{c^2} } }[/tex]
=1.02 x 5
t₁= 5.1 years
C ) Given t = 10 years , t₁ = ? v = .8c
[tex]\frac{10}{\sqrt{1-\frac{.64c^2}{c^2} } }[/tex]
=1.67 x 10
t₁= 16.7 years
D ) Given t = 10 years , t₁ = ? v = .4c
[tex]\frac{10}{\sqrt{1-\frac{.16c^2}{c^2} } }[/tex]
=1.09 x 10
t₁= 10.9 years
E ) Given t = 20 years , t₁ = ? v = .8c
[tex]\frac{20}{\sqrt{1-\frac{.64c^2}{c^2} } }[/tex]
=1.67 x 20
t₁= 33.4 years
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