Ditch crossing is one of the essential capabilities required for a biped robot in disaster management and search and rescue operations. Present work focuses on crossing a wide ditch with landing uncertainties by an under-actuated planar biped robot with five degrees of freedom. We consider a ditch as wide for a robot when the ankle to ankle stretch required to cross it is at least equal to the leg length of the robot. Since locomotion in uncertain environments requires real-time planning, in this paper, we present a new approach for generating real-time joint trajectories using control constraints not explicitly dependent on time, considering impact, dynamic balance, and friction. As part of the approach, we introduce a novel concept called the point of feasibility for bringing the biped robot to complete rest at the end of ditch crossing. We present a study on the influence of initial posture on landing impact and net energy consumption. Through simulations, we found the best initial postures to efficiently cross a wide ditch of width 1.05 m, with less impact and without singularities. Finally, we demonstrate the advantage of the proposed approach to cross a wide ditch when the surface friction is not same on both sides of the ditch.