P$3$: $(10$ marks$)$

The spring $(k=500\frac{N}{m})$ shown in the Figure below is compressed $30\mathrm{.}0$ cm from its equilibrium position by a $0\mathrm{.}500-kg$ box. After being launched from rest, the box moves across a horizontal surface and then onto inclined plane at point A until momentarily stops at the top of the plane at height $(H)$ at point B $.$ If both the inclined plane and the horizontal surface are frictionless. Determine the followings:$-$

B

$($a$)$ The speed of the blook just befor it enters the inclined plane at point A $.$

$($b$)$ The hight of the block at the top of the plane at point B $,$ where the object stops.