$[10$ points$]$ A $2\mathrm{.}5$ kg block is held in place against a spring $($spring is compressed by $4\mathrm{.}0$ cm $)$ at point A in the diagram below. After releasing the force, the block is projected with a velocity $v_1=2\mathrm{.}20\frac{m}{s}$ upon separation from the spring.

$($a$)[5$ points$]$ Find the spring constant of the spring.

$($b$)[5$ points$]$ If the height of the frictionless ramp is $36$ cm $,$ what is the speed of the block at the bottom?