Final answer:
According to the principle of conservation of momentum, the total momentum of an isolated system remain constant. The velocity of recoil of the gun is -72 m/s, and the total energy of the gun and the bullet is 285,120 J.
Step-by-step explanation:
To find the velocity of recoil of the gun, we can use the concept of conservation of momentum. According to this principle, the total momentum of an isolated system remains constant. In this case, the initial momentum of the bullet and gun system is zero (since they were at rest before separation) and after firing, the final momentum of the bullet and gun system should also be zero. This can be expressed as:
Initial momentum = Final momentum
The initial momentum of the bullet is given by:
Initial momentum of bullet = mass of bullet * muzzle velocity of bullet
Plugging in the values, we get:
0 = (10 g)(720 m/s) + (10 kg)(velocity of recoil)
Solving for the velocity of recoil, we find that it is equal to -72 m/s. The negative sign indicates that the gun recoils in the opposite direction of the bullet's motion.
To find the total energy of the gun and the bullet, we can use the equation for kinetic energy:
Kinetic energy = (1/2) * mass * velocity^2
The kinetic energy of the bullet is:
Kinetic energy of bullet = (1/2)(10 g)(720 m/s)^2
Plugging in the values, we get:
Kinetic energy of bullet = 259,200 J
The kinetic energy of the gun (recoil energy) is:
Kinetic energy of gun = (1/2)(10 kg)(-72 m/s)^2
Plugging in the values and squaring the velocity, we get:
Kinetic energy of gun = 25,920 J
The total energy of the gun and the bullet is the sum of their respective kinetic energies:
Total energy = Kinetic energy of bullet + Kinetic energy of gun
Substituting the values, we get:
Total energy = 259,200 J + 25,920 J
Total energy = 285,120 J