A $2-$kg block is given an initial speed, $v_A,$ at point A and begins to slide down an inclined surface having a coefficient of kinetic friction, ${}_k=0\mathrm{.}25.$ A spring of constant $k=50\frac{N}{m},$ located down the inclined surface, is constrained by the plate using cables attached to the wall so that its length is $50cm.$ If the block is given an initial velocity $v_A=1\frac{m}{s}$ and it pushes the plate forward $15cm$ before stopping, determine the spring's unstretched length, $l_0.$ Neglect the mass of the plate and spring.