A cannon is rigidly attached to a carriage, which can move along horizontal rails, but is connected to a post by a large spring, initially unstretched and with force constant k = 1.87 ✕ 104 N/m, as in the figure below. The cannon fires a 200-kg projectile at a velocity of 126 m/s directed 45.0° above the horizontal.


(a) If the mass of the cannon and its carriage is 5000 kg, find the recoil speed of the cannon. 

(b) Determine the maximum extension of the spring. 

(c) Find the maximum force the spring exerts on the carriage. (Enter the magnitude of the force.) 

(d) Consider the system consisting of the cannon, the carriage, and the shell. Is the momentum of this system conserved during the firing?

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