Kinetic energy = 0.5 * m * v²
m mass
v velocity
If the velocity stays the same and the kinetic energy goes down by a factor of 2, the mass must go down by a factor of 2 also.
B) The amount of work done
The conservation of momentum states that the total momentum in a system is constant if there is no external force acting on the system. The total momentum in the gun bullet system is 0 so it must stay that way.
The momentum of the bullet is mv = 0.015*500=7.5
The momentum of the gun must be the same to keep the total momentum of the system equal to zero, so we know that p = 7.5 for the gun.
Substituting this in we get:
7.5=3.1x
x=7.5/3.1
x=2.42
So the speed of the gun is 2.4m/s.
