Question

A spaceship 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.

Answer 1

`t'=1.1897*10^(-6) s`

t'=1.1897 μs

Step-by-step explanation:

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

Formula:

`u=(u'+v)/(1+(u'*v)/(c^(2)))`

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'=(v-u)/((u*v)/(c^(2) )-1 )`

`u'=(-0.82c-0.82c)/((0.82c*(-0.82c))/(c^(2) )-1 )`

u'=0.9806c

Time for micrometeorite to pass spaceship can be calculated as:

`t'=(length)/(Relatie seed (u'))`

`t'=(350)/(0.9806c)` (c = 3*10^8 m/s)

`t'=(350)/(0.9806* 3.0*10^(8) )`

`t'=1.1897*10^(-6) s`

t'=1.1897 μs