Problem $4$

A projectile launcher $($as done in our lab$)$ uses a spring with a force constant of $300\frac{N}{m}$ to propel a $10\mathrm{.}0$ g steel ball. The projectile launcher is placed at the edge of a table and is shot horizontally. If the spring is compressed $7\mathrm{.}00$ cm and friction is negligible:

a$)$ How much force is needed to compress the spring $7\mathrm{.}00$ cm $?$

b$)$ What was the work done on the spring to compress it $7\mathrm{.}00$ cm $?$

c$)$ What is the speed of the $10\mathrm{.}0$ g steel ball when it leaves projectile launcher?

d$)$ The steel ball is $1\mathrm{.}20$ m above the floor when the ball is shot from the launcher. Using conservation of energy, what is the speed of the ball at the moment the ball lands on the floor?