Final answer:
The question involves applying the conservation of momentum principle to calculate the change in velocity of a ship after it fires an artillery shell. The recoil velocity is found by equating the momenta before and after the event, and rearranging the equation to solve for the new velocity of the ship.
Step-by-step explanation:
The student's question involves the conservation of momentum when a large ship fires an artillery shell. The ship and shell together form an isolated system, and thus, the total momentum before and after the firing must be the same. Given the momentum of the ship and the shell fired from it, one can calculate the change in the ship’s velocity using the principle of conservation of momentum.
Calculating the Recoil Velocity of the Ship-
Let the original momentum of the ship be pship and the momentum of the fired shell be pshell. Before the firing, the total momentum is just the ship's momentum. After firing, the total momentum is the sum of the momentum of the ship (now at a lower speed) and the momentum of the shell. To find the new velocity of the ship, v'ship, after the shell has been fired, we use the following equation:
Momentum before firing = Momentum after firing
pship = mship × v'ship + mshell × vshell
By rearranging and solving for v'ship, we can find how much slower the ship is traveling after firing the shell.