Answer:
The contracted length as measured is 22.22 m
Solution:
As per the question:
Speed of the rockets, v = 0.8c
Length of the rocket, L = 100 m
Now,
To calculate the length of rocket A w.r.t rocket B:
The relative speed of the rockets A and B approaching the earth from the opposite directions:
[tex]Relative speed,\ v_{r} = \frac{- 0.8c - 0.8c}{1 + \frac{v^{2}}{c^{2}}}[/tex]
[tex]v_{r} = \frac{- 1.6c}{1 + \frac{(0.8c)^{2}}{c^{2}}} = 0.975c[/tex]
The contracted length is given by:
[tex]L' = \frac{L}{\sqrt{1 - \frac{v_{r}^{2}}{c^{2}}}}[/tex]
[tex]L' = \frac{100}{\sqrt{1 - \frac{(0.975c)^{2}}{c^{2}}}} = 22.22\ m[/tex]
