Respuesta :
Answer:
proper time taken by the person is 9.911 × 10⁻⁵ s
Explanation:
speed of the person in x- direction = 40,000 km/s
= 40,000 × 10³ m/s
= 4 × 10⁷ m/s
when the person just passes the street lamp is switched on which is at x =4 km
Lorentz factor = [tex]\gamma = \dfrac{1}{\sqrt{1-\dfrac{r^2}{c^2}}}[/tex]
= [tex]\dfrac{1}{\sqrt{1-\dfrac{(4 \times 10^7)^2}{(3 \times 10^8)2}}}[/tex]
= 1.009
time taken in your frame of reference,t =[tex]\dfrac{D}{v}[/tex]
=[tex]\dfrac{4}{40000} = 10 ^{-4}s[/tex]
proper time =[tex] t_0 = \dfrac{t}{\gamma}=\dfrac{10^{-4}}{1.009}= 9.911 \times 10^{-5} s[/tex]
hence, proper time taken by the person is 9.911 × 10⁻⁵ s
