a$)$ First, they consider an anti$-$matter bomb. $$If the bomb needs to produce an explosion energy$$of $1024$joules to destroy the station, how much antimatter mass do they need for their bomb?

$($b$)$ Next they consider destroying it by launching a small black hole$$into its interior. $$They decide$$that the black hole must have a$$Schwarzschild radius of at least $3$ x$10-10$m $($about the size$$of an$$atom$)$ or else it would pass through without doing much damage. How massive would the black$$hole need to be for the Schwarzschild radius$$to be this large?

$($c$)$ After deciding the first two methods were too complicated, they decide to just throw$$a big rock$$at it$.$ They determine the asteroid needs to be traveling at $1000$ km$/$s$$or the space station will$$have time to deflect it$.$Assuming the kinetic energy at impact$$needs to be at least $1024$joules$,$ how$$massive of an asteroid do they need?