$1-$ When the Starship Enterprise travels at impulse $($v $=0\mathrm{.}7$c$),$ a ground based observer measures the ship as $707$ ft long. How long does the crew measure the ship? $2-$ If you were on a spaceship travelling at $0\mathrm{.}50$c away from a star, what speed would the starlight pass you? $3-$ A spaceship travels at $0\mathrm{.}99$c for $3$ years ship time. How much time would pass on the Earth? $4-$ A neon sign in front of a caf$$ flashes on and off once every $4\mathrm{.}1$ s$,$ as measured by the head cook. How much time elapses between flashes of the sign as measured by an astronaut in a spaceship moving toward Earth With a speed of $0\mathrm{.}84$c$?5-$ Spacecraft Alpha is moving at $0\mathrm{.}90$c with respect to the earth. If spacecraft Beta is to pass Alpha at a relative speed of $0\mathrm{.}50$c in the same direction, what speed must Beta have with respect to the earth? $6-$ At what speed does the kinetic energy of a particle equal its rest energy? A meter stick moving with respect to an $-7$ observer appears only $500$ mm long to her. What is its relative speed