A set of twins,Andrea and Courtney,are initially 10 years old.While Courtney remains on Earth,Andrea rides on a spaceship that travels away from Earth at a speed of 0.60c for 10 years (as measured by Courtney).At the end of the trip,Courtney is 20 years old.How old is Andrea?
A)10 years
B)12 years
C)18 years
D)20 years

Question

Quizplus · Accepted Answer

According to the time dilation formula, the time experienced by Andrea on the spaceship can be calculated as follows:
Δt_A = Δt_C/√(1 - v^2/c^2)
where
Δt_A = time experienced by Andrea on the spaceship
Δt_C = time experienced by Courtney on Earth
v = velocity of spaceship relative to Earth = 0.60c
c = speed of light
Putting in the values, we get:
Δt_A = 10/√(1 - (0.60c)^2/c^2)
Δt_A = 10/√(1 - 0.36)
Δt_A = 10/0.8
Δt_A = 12.5 years (rounded off to one decimal place)
Therefore, Andrea is 12.5 years old at the end of the trip.

A Set of Twins,Andrea and Courtney,are Initially 10 Years Old