Question

The U.S.S. Constitution, the oldest fully commissioned war ship in the world, is docked in Boston, Massachusetts. Also known as Old Ironsides for her seemingly impenetrable hull, the frigate houses 56 pieces of heavy artillery. Mounted on bearings that allow them to recoil at a speed of 1.75 m/s are 20 carronades, each with a mass of 1100 kg. If a carronade fires a 15 kg cannonball straight ahead, with what muzzle velocity does the cannonball leave the cannon?

Answer 1

The muzzle velocity of the cannonball leaving the cannon is 129.17 m/s.

Step-by-step explanation:

To calculate the muzzle velocity with which the cannonball leaves the cannon, we need to use the principle of conservation of momentum. The momentum before firing the cannonball is zero since both the carronade and the cannonball are stationary. After firing the cannonball, the momentum should still be zero. The formula for momentum is given by: momentum = mass × velocity.

Let's assume the muzzle velocity of the cannonball is V. Since the carronade and cannonball are mounted on bearings, they can recoil at a speed of 1.75 m/s. This means the recoil velocity of the carronade is -1.75 m/s (negative sign indicates opposite direction).

Using the conservation of momentum, we can set up the equation as follows:

0 = (1100 kg × -1.75 m/s) + (15 kg × V)

Rearranging the equation, we can solve for V:

V = (-1100 kg × -1.75 m/s) / 15 kg

V = 129.17 m/s

Therefore, the muzzle velocity with which the cannonball leaves the cannon is 129.17 m/s.