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 \(\text{m/s}\)) if air drag is negligible and the frictional force is independent of speed?

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