To determine the recoil velocity of the cannon, we can use the principle of conservation of momentum. This principle states that the total momentum of a system of objects is conserved if there are no external forces acting on the system.
In this case, the system consists of the cannon and the cannonball. Before the cannonball is fired, the total momentum of the system is zero. After the cannonball is fired, the momentum of the cannonball is equal in magnitude but opposite in direction to the momentum of the cannon.
We can use the following equation to solve for the recoil velocity of the cannon:
m1v1 + m2v2 = (m1 + m2)v
where
m1 = mass of the cannonball = 5.0 kg
v1 = velocity of the cannonball before firing = 0 m/s (since it is initially at rest)
m2 = mass of the cannon = 160 kg
v2 = velocity of the cannon before firing = 0 m/s (since it is initially at rest)
v = recoil velocity of the cannon (unknown)
Plugging in the given values, we get:
(5.0 kg)(0 m/s) + (160 kg)(0 m/s) = (5.0 kg + 160 kg)v
Simplifying, we get:
0 kg m/s = (165 kg)v
Dividing both sides by 165 kg, we get:
v = 0 m/s
Therefore, the recoil velocity of the cannon is zero.