To calculate the applied retarding force on a 30kg iron ball that falls from 30m and penetrates 8m into the ground, one must first determine the ball's velocity upon impact using gravitational equations. The kinetic energy at impact can be calculated, and then the work done by the retarding force can be equated to this energy to find the force. There is a suggestion to verify the penetration depth, as 8m seems excessive and might be a typographical error for 8mm. The discussion emphasizes the importance of using standard equations and showing work in the solution process. Accurate calculations are crucial for determining the retarding force effectively.