battleship that is 6.00×107 kg and is originally at rest fires a 1100-kg artillery shell horizontally with a velocity of 575 m/s. (a) If the shell is fired straight aft (toward the rear of the ship), there will be negligible friction opposing the ship’s recoil. Calculate its recoil velocity. (b) Calculate the increase in internal kinetic energy (that is, for the ship and the shell). This energy is less than the energy released by the gunpowder—significant heat transfer occurs.
Step-by-step solution In this problem a battleship fires an artillery shell calculate its recoil velocity ,calculate the increase in the kinetic energy and the energy release release by the gunpowder as per the given data respectively: Step 1 of 3 Apply law of conservation of linear momentum to find the recoil velocity of the battleship. Step 2 of 3 Initially, the momentum of the system is zero and after the ship fires the artillery shell, both shop and shell moves with equal but opposite momentum to conserve the linear momentum. That means, the final linear momentum of the system is zero. Here, is the velocity of the shell of mass and is the velocity of the ship of mass . Rearrange the equation for . Here, the negative sign indicates that the recoil velocity of the ship. Substitute for , for , and for . Therefore, the recoil velocity of the battle ship in two significant figures is .