One 20-year-old twin brother takes a space trip with a speed of 0.80c for 30 years according to a clock on his spaceship.At the end of this trip,what are (a)his own age and (b)the age of his Earth-based twin brother?
A)(a)20 y (b)30 y
B)(a)30 y (b)50 y
C)(a)50 y (b)70 y
D)(a)70 y (b)90 y

Question

Quizplus · Accepted Answer

According to the theory of relativity, time dilation occurs as an object approaches the speed of light. The faster the object moves, the slower time passes for it relative to a stationary observer. In this case, the twin brother traveling at 0.8c experiences time dilation, meaning that time passes slower for him compared to his twin brother on Earth.

Using the formula t' = t/√(1-v^2/c^2), where t' is the time dilation experienced by the traveling twin, t is the time experienced by the Earth-bound twin, v is the velocity of the traveling twin, and c is the speed of light, we can calculate the age difference between the two twin brothers.

Plugging in v = 0.8c, t = 30 years, and t' = ? into the formula, we get:

t' = t/√(1-v^2/c^2)
t' = 30/√(1-0.8^2)
t' = 30/√(0.36)
t' = 30/0.6
t' = 50 years

Therefore, the traveling twin brother will age 50 years while his Earth-based twin brother will age 70 years (20 years older than the traveling twin brother). The best choice is C.

One 20-Year-Old Twin Brother Takes a Space Trip with a Speed