# Calculating Recoil Velocity of a Cannon

• TT0
In summary, based on the conservation of momentum formula, the initial velocity of recoil of the 600kg cannon can be found by setting the initial momentum of the cannon and the cannonball equal to the final momentum of the cannon and the cannonball. Solving for the recoil velocity, it is determined to be -15 m/s, with the negative sign indicating the direction of recoil. This can be explained by Newton's third law, where the force exerted by the cannonball on the cannon is equal in magnitude but opposite in direction to the force exerted by the cannon on the cannonball.
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

TT0 said:
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

## What is the formula for calculating recoil velocity of a cannon?

The formula for calculating recoil velocity of a cannon is: recoil velocity = (mass of projectile x velocity of projectile) / mass of cannon.

## Why is it important to calculate recoil velocity of a cannon?

Calculating recoil velocity of a cannon is important because it helps determine the amount of force and energy exerted on the cannon and its surroundings. This information can be used to properly design and operate the cannon for safety and effectiveness.

## What factors affect the recoil velocity of a cannon?

The recoil velocity of a cannon is affected by the mass and velocity of the projectile, as well as the mass of the cannon itself. Other factors such as air resistance and friction may also play a role in the recoil velocity.

## How does the recoil velocity of a cannon impact its accuracy?

The recoil velocity of a cannon can impact its accuracy by causing the cannon to move or shake, resulting in a deviation from the intended trajectory of the projectile. Properly calculating and managing recoil velocity can help improve the accuracy of a cannon.

## What are some applications of calculating recoil velocity of a cannon?

Calculating recoil velocity of a cannon is important in military and defense applications, as well as in recreational activities such as hunting and shooting sports. It is also used in engineering and physics studies to understand the principles of projectile motion and energy transfer.

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