Calculating Recoil Velocity of a Cannon

[TT0]

Homework Statement

A 20kg cannon ball is fired from a 600kg cannon, with an initial velocity of 450 m/s. Calculate the initial velocity of recoil of the cannon.

Homework Equations

Conservation of momentum formula

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

where
m = mass
u = initial velocity
v = final velocity

The Attempt at a Solution

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

let v = recoil velocity

20 x 0 + 600 x 0 = 20 x 450 + 600 x v
0 = 9000 + 600v
-9000 = 600v
v = -15 m/s

The negative is from the negative direction so the answer is 15 m/s. Is my logic correct, because I know how momentum is conserved, but is this the right way to think about it? Also how can Newton's law explain this?

Thanks

 

[ArmanCham]

The negative is from the negative direction so the answer is 15 m/s. Is my logic correct, because I know how momentum is conserved, but is this the right way to think about it? Also how can Newton's law explain this?

Yeah your idea is correct to solve this problem. Newton third law says
"When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body."
This is the thing happens here.You exert a force and cannon ball fired.Canon ball goes forward but canon goes back for this affect.Newton third law explain this easily.

 

[TT0]

Ok thanks a lot