$($B$)($i$)(5$ points$)$ A spaceship, while stationary on Earth, is $100$ m long. How long $($in meters$)$ does this spaceship look to observers on Earth, when it is moving away from Earth at a speed of $0\mathrm{.}5$c$?[$Hint: Assume Earth is stationary. This is a good approximation here, since the Earths motion is nowhere close to relativistic or in other words, nowhere close to being fast enough for relativistic e ects become noticeable.$]($ii$)(5$ points$)$ As the spaceship travels away from Earth at a speed of $0\mathrm{.}5$c$,$ it launches a probe away from Earth. The probe is traveling at a speed of $0\mathrm{.}75$c relative to the spaceship. What velocity do observers on Earth measure for the probe? $($iii$)(5$ points$)$ If the spaceship has a mass of $1\mathrm{.}0103$ kg$,$ what is the momentum of the spaceship, as observed from Earth, when the spaceship is moving away from Earth at $0\mathrm{.}5$c$?($iv$)(5$ points$)$ What is the total energy of the spaceship, as observed from Earth, when the spaceship is moving away from Earth at $0\mathrm{.}5$c$?$