A cannon with a mass of 10 tons fires a bullet horizontally with a mass of 50kg. The velocity of the bullet when it leaves the barrel of the cannon is 800 m / s. calculate the recoil velocity of the cannon.

To calculate the recoil velocity of the cannon, we can use the principle of conservation of momentum. According to this principle, the total momentum before the firing of the bullet is equal to the total momentum after the firing.

Before the firing:
The initial momentum of the cannon and bullet system is given by the equation:
Initial Momentum = (Mass of Cannon) × (Initial Velocity of Cannon) + (Mass of Bullet) × (Initial Velocity of Bullet)

Given:
Mass of cannon (m1) = 10000 kg
Initial velocity of bullet (v2) = 800 m/s
Mass of bullet (m2) = 50 kg

Now we can substitute these values into the equation to find the initial momentum of the system:
Initial Momentum = (10000 kg) × (0 m/s) + (50 kg) × (800 m/s)
Initial Momentum = 40000 kg·m/s

After the firing:
The final momentum of the cannon and bullet system is given by the equation:
Final Momentum = (Mass of Cannon) × (Final Velocity of Cannon) + (Mass of Bullet) × (Final Velocity of Bullet)

Since the bullet is fired horizontally, its final velocity is 0 (assuming no air resistance). Therefore, the equation becomes:
Final Momentum = (Mass of Cannon) × (Final Velocity of Cannon) + (Mass of Bullet) × (0 m/s)
Final Momentum = (Mass of Cannon) × (Final Velocity of Cannon)

Let's assume the recoil velocity of the cannon is v1. So the final velocity of the cannon can be written as -v1 (negative since it is in the opposite direction to the bullet's velocity).

Now we can substitute the given values into the equation to find the final momentum of the system:
Final Momentum = (10000 kg) × (-v1 m/s)

According to the principle of conservation of momentum, the initial momentum of the system is equal to the final momentum of the system:
Initial Momentum = Final Momentum

Equating the initial and final momenta:
40000 kg·m/s = (10000 kg) × (-v1 m/s)
-4 m/s = -v1

Thus, the recoil velocity of the cannon is 4 m/s in the opposite direction to the bullet's velocity.