A small alien scout ship $($mass $=500kg)$ accidentally enters Earth's atmosphere directly above a trampoline park in New Mexico. Their anti$-$gravity fails, causing them to fall from a height of $30$ m $.$ Fortunately, they land perfectly on a large competitiongrade trampoline with spring constant $k=15,000\frac{N}{m}.$

$($a$)(7$ pts$)$ Calculate the maximum distance the trampoline deforms before the ship momentarily comes to rest.

$($b$)(7$ pts$)$ What is the peak force exerted on the alien ship by the trampoline during this compression?

$($c$)(7$ pts$)$ Unfortunately the manufacturer did not follow best practices for building the trampoline netting. It used a cheaper version of the material, which fails after the trampoline has only deformed by $1$ m $.$ How fast is the ship moving immediately after breaking through the trampoline?