Answer:
[tex]t'=1.1897*10^{-6} s[/tex]
t'=1.1897 μs
Explanation:
First we will calculate the velocity of micrometeorite relative to spaceship.
Formula:
[tex]u=\frac{u'+v}{1+\frac{u'*v}{c^{2}}}[/tex]
where:
v is the velocity of spaceship relative to certain frame of reference = -0.82c (Negative sign is due to antiparallel track).
u is the velocity of micrometeorite relative to same frame of reference as spaceship = .82c (Negative sign is due to antiparallel track)
u' is the relative velocity of micrometeorite with respect to spaceship.
In order to find u' , we can rewrite the above expression as:
[tex]u'=\frac{v-u}{\frac{u*v}{c^{2} }-1 }[/tex]
[tex]u'=\frac{-0.82c-0.82c}{\frac{0.82c*(-0.82c)}{c^{2} }-1 }[/tex]
u'=0.9806c
Time for micrometeorite to pass spaceship can be calculated as:
[tex]t'=\frac{length}{Relatie seed (u')}[/tex]
[tex]t'=\frac{350}{0.9806c}[/tex] (c = 3*10^8 m/s)
[tex]t'=\frac{350}{0.9806* 3.0*10^{8} }[/tex]
[tex]t'=1.1897*10^{-6} s[/tex]
t'=1.1897 μs
