Children sliding down a hill

Two children stand on a large sloping hillside that can be considered as a plane. The angle of the incline of the hillside is $\alpha$. The ground is just sufficiently icy that a child would slide downhill with uniform speed as a result of receiving even the slightest impulse down the hill.

For fun, one of the children (leaning against a tree) pushes the other child with a horizontal initial speed of $v_0 = \SI{1}{m/s}$, who then slides down the slope, as indicated by the curved arrow. What will be this child's final speed (in $\si{m/s}$) if air drag is negligible and the frictional force is independent of speed?