Two thin rods each of mass m and length l are connected to an ideal (no friction) hinge an...

Two thin rods each of mass m and length l are connected to an ideal (no friction) hinge and a horizontal thread. The system rests on a smooth surface as shown in the figure. At time t = 0, the thread is cut. Neglecting the mass of the hinge and the thread, and considering only motion in the xy plane

(a) Find the speed at which the hinge hits the floor.

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(b) Find the time it takes for the hinge to hit the floor.