In Jules Verne's classic Around the World in Eighty Days,Phileas Fogg travels around the world in,according to his calculation,81 days.Due to crossing the International Date Line he actually made it only 80 days.How fast would his descendent have to travel in his space ship in order for time dilation to make 7.0 days in his frame be measured as 8.0 days to observers on the Earth?
A)0.23 c
B)0.35 c
C)0.48 c
D)0.88 c
E)0.94 c

Question

Quizplus · Accepted Answer

We use the formula for time dilation:
t' = t/sqrt(1-v^2/c^2)
where t is the time interval in the observer's frame, t' is the time interval in the moving frame, v is the velocity of the moving frame relative to the observer, and c is the speed of light.
Let t = 7.0 days and t' = 8.0 days.
Thus, 8.0 = 7.0/sqrt(1-v^2/c^2)
Solving for v/c, we get
v/c = sqrt(1 - (7.0/8.0)^2) = 0.48
Therefore, his descendent would have to travel at 0.48 times the speed of light, or 0.48c.

In Jules Verne's Classic Around the World in Eighty Days,Phileas