A500.0-kilogram cannon is at rest on a frictionless surface. a remote triggering device causes a 5.0-kilogram projectile to be fired from the cannon moving at 30 m/s. what is the recoil speed of the cannon? a. 83.3 m/s b. 0.3 m/s c. 16.7 m/s d. 75 m/s

From the law of conservation of momentum the initial momentum is equivalent to the final momentum. Therefore, the total momentum before firing will be equivalent to the momentum after firing. if we take mass of the projectile to be mass i and that of the cannon as mass ii.
The initial momentum will be given by m1v1 +m2v1 
This initial momentum is equivalent to zero since initially both the cannon and the projectile are at zero velocity.
The final momentum is given by m1v2 + m2v3, where v2 is the velocity of the projectile  and v3 is the recoil velocity of the cannon.
Therefore, m1v2 + m2v3 =0
              ( 5 × 30 ) + ( 500 × v3) =0
               500 v3 = -150
                       v3 =  - 0.3 m/s
The velocity is negative indicating that the cannon moved in the opposite direction. therefore, the recoil velocity is 0.3 m/s