Aspaceship whose rest length is 350m has a speed of .82c
withrespect to a certain reference frame. a micrometeorite also
withspeed .82c in this frame, passes the spaceship on an
antiparalleltrack. how long does it take this object to pass the
ship asmeasured from the ship.

t'=1.1897 μs

Explanation:

First we will calculate the velocity of micrometeorite relative to spaceship.

Formula:

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:

u'=0.9806c

Time for micrometeorite to pass spaceship can be calculated as:

    (c = 3*10^8 m/s)

t'=1.1897 μs