Time dilation: A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a spaceship which travels away from Earth at a speed of 0.60c for five years (as measured by Courtney), then immediately turns around and comes back at 0.60c. When Andrea returns, Courtney is 20 years old. How old is Andrea upon her return?
A) 10 y
B) 12 y
C) 15 y
D) 18 y
E) 20 y

Question

Quizplus · Accepted Answer

Time dilation is a phenomenon in which time passes slower for an observer who is moving relative to another observer. In this case, Andrea is moving relative to Courtney, so time will pass slower for Andrea. The time dilation equation is:```t' = t / γ```where:* t' is the time measured by the moving observer* t is the time measured by the stationary observer* γ is the Lorentz factor, which is given by:```γ = 1 / sqrt(1 - v^2/c^2)```where:* v is the speed of the moving observer* c is the speed of lightIn this case, Andrea is moving at a speed of 0.60c, so the Lorentz factor is:```γ = 1 / sqrt(1 - 0.60^2/c^2) = 1.25```This means that time will pass 1.25 times slower for Andrea than for Courtney. So, when Courtney is 20 years old, Andrea will be:```t' = 20 years / 1.25 = 16 years```Therefore, Andrea is 16 years old upon her return.

Time Dilation: a Set of Twins, Andrea and Courtney, Are