A 3 kilograms mass is sliding down a frictionless inclined plane, theta, the angle of this inclined plane is 22 degrees, towards a spring with constant stiffness of 450 Newtons per meter. The mass is initially a meter from the spring and travels at a speed of 0.8 meters per second. Assume the mass of the spring is negligible. How much is the spring compressed when the mass is momentarily stationary? 

Old naval ships fired cannonballs from a cannon. It was crucial to stop the cannon’s recoil; otherwise, the heavy cannon would go careening across the ship’s deck. In one design, a large spring was placed behind the cannon. The other end of the spring braced against a post firmly anchored to the ship’s frame. Firing the cannon can compress the spring. At this stage, we can assume the cannonball is already fired and completely out of the cannon. How fast could this cannon fire cannonballs?