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Relativity -- rocket problems
Consider two rockets, each of rest length 100 meters. Rocket 1 is at rest in frame S and has its nose at x=0 and its tail at x=+100 meters. Rocket 2 is at rest in frame S’ and has its nose at x’=0 and its tail at x’=
-100 meters.
Now suppose that frame S’ moves with speed V in the x+ direction relative to frame S.
Event A: The nose of Rocket 2 passes the nose of Rocket 1 at time tA = t'A = 0
Event B: The tail of Rocket 2 passes the nose of Rocket 1 at time tB = 2.5 microseconds in frame S.
Use the information about event B to calculate the speed V of S’ relative to S.
v=d/t
[tex]L = \frac{{L_0 }}{\gamma } = L_0 \sqrt {1 - \frac{{v^2 }}{{c^2 }}} [/tex]
[tex]T = T_0 \gamma = \frac{{T_0 }}{{\sqrt {1 - \frac{{v^2 }}{{c^2 }}} }}[/tex]
v=100m / 2.5 microseconds = 40*106 m/s
What doesn't make sense to me is that I used 100 m for d, yet there should be length contraction. So shouldn't I be using a different d? But how do I get that d if I don't know V?
Homework Statement
Consider two rockets, each of rest length 100 meters. Rocket 1 is at rest in frame S and has its nose at x=0 and its tail at x=+100 meters. Rocket 2 is at rest in frame S’ and has its nose at x’=0 and its tail at x’=
-100 meters.
Now suppose that frame S’ moves with speed V in the x+ direction relative to frame S.
Event A: The nose of Rocket 2 passes the nose of Rocket 1 at time tA = t'A = 0
Event B: The tail of Rocket 2 passes the nose of Rocket 1 at time tB = 2.5 microseconds in frame S.
Use the information about event B to calculate the speed V of S’ relative to S.
Homework Equations
v=d/t
[tex]L = \frac{{L_0 }}{\gamma } = L_0 \sqrt {1 - \frac{{v^2 }}{{c^2 }}} [/tex]
[tex]T = T_0 \gamma = \frac{{T_0 }}{{\sqrt {1 - \frac{{v^2 }}{{c^2 }}} }}[/tex]
The Attempt at a Solution
v=100m / 2.5 microseconds = 40*106 m/s
What doesn't make sense to me is that I used 100 m for d, yet there should be length contraction. So shouldn't I be using a different d? But how do I get that d if I don't know V?