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

v = 0.92 c

Step-by-step 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-(v^2)/(c^2)}} \\\\\\\sqrt{1-(v^2)/(c^2)}=(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-(v^2)/(c^2)} = (4\ years)/(10\ years)\\\\ 1-(v^2)/(c^2)=((2)/(5))^2\\\\(v^2)/(c^2) = 1-(4)/(25)\\\\(v^2)/(c^2) = (21)/(25)\\\\v^2 = 0.84c^2\\\\`

v = 0.92 c