This is a simple problem of two-dimensional mechanics. Forces in the X-direction, (drag action on the projectile) are assumed to be zero - that motion is uniform. However gravity acts in the Z-component.

Point Blank The warships (80 yards apart - perfectly abreast) are in the firing position Lord Nelson's crews called "point-blank." Suppose ship A fires a cannon, aimed perfectly horizontal, at ship B. The mass of the shot is 24 pounds. Assume its muzzle speed is constant over its flight ~ 500 ft/s. The origin is the muzzle of the firing cannon. The extrinsic properties of the shot an instant before it impacts the ship (t = t-impact) are its position, velocity, and kinetic energy. The momentum equation with its initial and final conditions is given.

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Integrate the momentum equation and determine the velocity speed and momentum of the shot an instant before impact with ship B.

♦  Position:  We set our coordinate origin to be at the cannon muzzle in Ship A (See figure). Both ships move at near equal speeds on parallel courses. The differential equation and initial conditions for this event are:

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The above equation integrates twice to yield:

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With conditions applied, the equation becomes:

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Separate the equation into I and K components then solve.

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Thus after 0.48 seconds, the shot would be about to impact Ship B, 3.7 feet below the bore line of its cannons (assuming near identical ships).

♦  Velocity:  A single integration of the momentum equation gives:

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Inserting the time "instant prior to impact," 0.48s, the velocity just prior to impact is:

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♦  Kinetic Energy:   In coming to rest after impact with the ship, nearly the entire kinetic energy of the shot will be transfered to the target ship. That amount of energy is:

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