Question

Please Help!!!!

Your Best friend gets on a ship and travels away fast. They return 10.0 years later and I’ve only aged 4.00 years. How fast was your friend traveling? Give your answer as ex. 0.5c

Answer 1

Answer:

v = 0.92 c

Explanation:

Here, we will use the time dilation formula from Einstein's theory of relativity to find the speed of traveling of the friend:

$t =\frac{t_o}{\sqrt{1-\frac{v^2}{c^2}}} \\\\\\\sqrt{1-\frac{v^2}{c^2}}=\frac{t_o}{t}$

where,

v = speed of traveling = ?

c = speed of light

t = time of return = 10 years

t₀ = time passed on earth = 4 years

Therefore,

$\sqrt{1-\frac{v^2}{c^2}} = \frac{4\ years}{10\ years}\\\\ 1-\frac{v^2}{c^2}=(\frac{2}{5})^2\\\\\frac{v^2}{c^2} = 1-\frac{4}{25}\\\\\frac{v^2}{c^2} = \frac{21}{25}\\\\v^2 = 0.84c^2$

v = 0.92 c