Velocity of child

Two children stand on a large, sloping hillside that can be considered as a plane. The ground is just sufficiently icy that a child would fall and slide downhill with a uniform speed as the result of receiving even the slightest impulse

For fun, one of the children (leaning against a tree) pushes the other with a horizontal initial speed v0=1m/s. The latter slides down the slope with a velocity that changes in both magnitude and direction. What will be the child’s final speed if air resistance is negligible and the frictional force is independent of the speed?