Spring gun with a spring constant $7200\frac{N}{m}$ is placed at the edge of a table which is a distance above the floor of $H=11\mathrm{.}25m.$ The spring gun is used to shoot $8kg-$marbles with a certain initial horizontal speed. The marble lands a distance $R=27m$ from the edge of the table. The mass of each marble is $m.$

a$.$ What is the speed of the marble at the edge of the table?

b$.$ What is the kinetic energy at the edge of the table?

c$.$ What is the initial compression of the spring gun?

d$.$ What is the total energy of the marble at the edge of the table with respect to floor level?

e$.$ What is the impact speed of the marble just before it strikes the floor?