The magnitude of the velocity of the cannon is 2.4m/s
Conservation of momentum:
According to the law of conservation of energy, the initial momentum of a system must be equal to the final momentum of the system.
Here the system is ball and cannon.
Let the mass of the ball be m = 8 kg
and the mass of the cannon be M = 1×10³ kg
The initial momentum (p) of the system is zero since both the ball and the cannon are at rest.
Given that the final momentum of the ball is 2.4 × 10³ kgm/s towards the east.
Lets east be the positive direction, then according to the conservation of momentum the cannon will have a recoil momentum towards the west equal to the momentum of the ball but in the negative direction, so that the final momentum is also zero.
Let the velocity of the cannon be v, then
2.4 × 10³ - 1×10³ × v = 0
2.4 × 10³ = 1×10³ × v
v = 2.4 m/s towards he west.
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