projectile, force of cannon

Question

1. Assume that every projectile fired by a toy cannon experiences a constant net force F along the entire length of the barrel. If a projectile of mass m leaves the barrel of the cannon with a speed v, at what speed will a projectile of mass 2m leave the barrel?
A) v/2
B) v/√2
C) v
D) 2v

Answer 1

The change of energy for the projectile is the work done on the projectile which is W = F*x where x is the barrel length.

This is the same no matter the mass of the projectile. As the projectile leaves the barrel it  has kinetic energy equal to F*x. The kinetic energy is the same no matter the mass.  

 

Set 1/2 * m*v1^2 = 1/2*2*m*v2^2 and solve for v2 in terms of v1