Lagging HingeJoints2D and DistanceJoints2D

I have a rope that is built out of HingeJoints2D. The last hinge joint is connected to the player. The player drags the rope. The rope falls behind. I tried using DistanceJoints2D but it still presents the same problem but is getting dragged way slower than the HingeJoints2D.

I have tried the verlet simulation for the rope; however, it doesn't calculate physics objects that are getting dropped on the rope as shown in this video. By far, verlet has provided a better looking rope but it doesn't offer physics simulation like HingeJoint2D and DistanceJoint2D does.

I cannot omit this from my game as this is the core game mechanic. Help would be greatly appreciated