To solve the physics problem of a 510-N swimmer diving off a cliff, the key is to determine the minimum horizontal speed required to clear a 1.75 m wide ledge located 9.00 m below. The swimmer is treated as a projectile launched horizontally from a height of 9 meters. The vertical motion can be described using the equation y = y_0 + v_0t + 0.5at^2, while the horizontal distance is calculated using x = u cos(θ) t. The swimmer's mass does not affect the calculations, as only the forces acting on her during the fall are considered. The solution involves applying these equations and performing algebraic manipulations to find the required speed.