Question

A cannon of mass 500 kg is loaded with a cannon ball of mass 1 kg. The cannon and ball are both stationary when the ball is fired at a velocity of 50 m/s. The cannon recoils when the gun is fired. What is the absolute value of the recoil velocity of the cannon?

Answer 1

The recoil velocity of the cannon is 5 m/s.

Step-by-step explanation:

The recoil velocity of the cannon can be calculated using the principle of conservation of momentum. According to this principle, the total momentum before firing is equal to the total momentum after firing. The momentum of an object is the product of its mass and velocity.

Before firing, both the cannon and the ball are stationary, so their initial momentum is zero. After firing, the cannon ball has a velocity of 50 m/s. Let's assume the recoil velocity of the cannon is v.

Using the principle of conservation of momentum, we can write the equation:

(mass of cannon x velocity of cannon) + (mass of ball x velocity of ball) = 0 + (mass of ball x velocity of ball)

Substituting the given values, we have:

(500 kg x -v) + (1 kg x 50 m/s) = 0 + (1 kg x 50 m/s)

Simplifying the equation:

500 kg x -v = 50 kg x 50 m/s

-500v = 2500

Dividing both sides by -500:

v = -5 m/s

The absolute value of the recoil velocity of the cannon is 5 m/s.