A cannon is rigidly attached to a carriage, which can move along horizontal rails, but is connected to a post by a large spring (with spring constant of 20,000.0 N/m), initially unstretched as shown in the figure. The cannon fires a 200.0-kg projectile directed at 45.0 degrees above the horizontal and the recoil causes the spring to stretch a distance of 1.80 m. Suppose that the mass of the cannon and its carriage (without the projectile) is 5000.0 kg and that the projectile is fired 3.00 meters above the surface. Determine the maximum height of the projectile. You may ignore air resistance, the kinetic friction of the carriage, and the rotational kinetic energy of the wheels.
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