Question

One of two 25-year-old identical twins begins a trip on a spaceship traveling at 0.8 c while her twin remains on Earth. The twin on Earth tracks her twin's trip for 10 years. After ten years, what age is the twin on the spaceship according to the twin on Earth?

Answer 1

Answer:

This equation is based on twin paradox - a phenomena where one of the twin travels to space at a speed close to speed of light and the other remains on earth. the twin from the space on return discovers that the one on earth age faster.

Solution:

$t_{o}$ = 10 years

v = 0.8c

c = speed of light in vacuum

The problem can be solved by time dilation equation:

$t = \frac{t_{o}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$            (1)

where,

t = time observed from a different inertial frame

Now, using eqn (1), we get:

$t = \frac{10}{\sqrt{1 - \frac{(0.8c)^{2}}{c^{2}}}}$

t = 16.67 years

The age of the twin on spaceship according to the one on earth = 25+16.67 =41.66 years