Question

a person named synchronises his clock with that of his assistant goes to a long journey in a rocket with velocity 0.999c. He returnes back when his clock reads one year.
then what time will be in his assistant clock?

Answer 1

hey mate.

given :

t = time in his assistant (improper time),
t0 = proper time

= 1 year,
v = 0.999c

to find = t :

According to Einstein's special relativity,

=) t = t0/√(1-v²/c²)

(by time dilation's principle)

=) t = 1/√(1-(0.999c)²/c²)



=) t = 1/√1-0.998001)

=) t = 1/√0.1999

= approx 22.7 years

hope it helps you!!

Answer 2

$\huge \bf{hey}$


$\huge { \mathfrak{here \: is \: answer}}$


given

velocity = 0.999c

speed of light= 299792458 m/s

or

3*10^8. m/s.... ( approx)

according to question


let the time in watch of his assistant be t'


formula

t'=

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



hence

$\bf{ \frac{1}{ \sqrt{1 - (\frac{0.999c}{c} )}^{2} } }$


hence.

the time in the watch

$\huge{ = \: 22.7 \: years}$

$\huge \boxed{ \boxed{ \boxed{hope \: it \: helps}}}$


$\huge{ \mathbb{THANKS}}$