During a full broadside, the ship might move sideways but the motion is insignificant at best.
An Iowa-class BB displaces about 57,000 tonnes (long or metric tons). An AP shell weighs about 1.22 tonnes and a full broadside would be just under 11 tonnes.
A full charge for each gun (WWII) is 660 lbs. of SPD 839 propellant. There is not enough energy in 3 tonnes of propellant to move 57,000 tonnes of ship any significant distance.
Hope this helps.
Garde la Foi, mes amis! Nous nous sommes les sauveurs de la République! Maintenant et Toujours!
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LonePalm, le Républicain du verre cassé (The Broken Glass Republican)
So the momentum of the BB, is equal to and opposite the combined momentum of the shells.
You've got a fairly large V (granted, it isn't anything like V2, but still...)
From a Goolag search.
They fired 2,700 pounds (1,225 kg) armor-piercing projectiles at a muzzle velocity of 2,500 ft/s (762 m/s), or 1,900 pounds (862 kg) high-capacity projectiles at 2,690 ft/s (820 m/s), up to 24 miles (21 nmi; 39 km).
(2700 lbs * 2500 ft/s ) shell * 9 shells = 6.075 x 10**7 ft*lb/s
the mass of the ship is 57,000 tonnes * 2204 lb/tonne =1.25628 x 10**8 lbs
Divide the momentum of the one side (shells), by the mass of the other (ship), to get the initial velocity of the ship:
1.25628 x 10 **8
6.075 x 10** 7
~= 2.0 ft/sec
That being said, there are other variables, such as the angle of the guns and the buoyancy of the ship in the water, together with the fact that water is fairly incompressible and will spring back.