The Dynamic Positioning System is used in offshore installations, such as drilling rigs and vessels, to maintain position without the need for anchoring. The DPS utilizes thrusters that adjust the vessel's position by counteracting environmental forces such as wind, waves, and currents.
Figure shows an inextensible catenary mooring cable in still water. The submerged weight (per meter length), and the anchor radius are 100 kg/m and 50 m, respectively. If horizontal tension ($T_h$) in the catenary is 1600 kg, the catenary length (AB) is ............. m (rounded to two decimal places). 