Once it leaves the bat, the club, or the hand, there is no horizontal force on it (ignoring air resistance). So it has no horizontal acceleration (ignoring air resistance).
We know that an athlete moves half of her body weight 250 N a distance of 20 cm. So: F = 250 N, d = 20 cm = 0.2 m The work formula: W = F * d W = 250 N * 0.2 m W = 50 J Answer: Her work after one push-up is 50 J.