a cannon with a mass of 1200 kilograms is positioned at the edge of a cliff where it fires a 100 kilogram cannonball horizontally. The cannonballs initial speed is 35 meters per second. What is the recoil of speed of the cannon.
To find the recoil speed of the cannon, we can apply the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, assuming no external forces are acting on the system.
In this scenario, we have two objects involved: the cannon and the cannonball. Let's denote the initial speed of the cannon as Vc (unknown) and the initial speed of the cannonball as Vb.
The total initial momentum before the cannon fires is given by:
Momentum_initial = (mass_cannon × Vc) + (mass_cannonball × Vb)
The momentum of the cannonball, being fired horizontally, can be calculated as:
Momentum_cannonball = mass_cannonball × Vb
Since the cannon is initially at rest (Vc = 0), the total initial momentum is simplified to:
Momentum_initial = (mass_cannonball × Vb)
Now, according to the conservation of momentum principle, the total momentum after the event should also be equal to Momentum_initial.
The momentum of the cannonball after being fired horizontally doesn't change, so:
Momentum_cannonball = mass_cannonball × Vb
To find the recoil speed of the cannon (Vc), we rearrange the equation:
Vc = (Momentum_initial - Momentum_cannonball) / (mass_cannon)
Substituting the given values:
Vc = [(mass_cannonball × Vb) - (mass_cannonball × Vb)] / (mass_cannon)
Vc = 0
Therefore, the recoil speed of the cannon is 0 m/s. This means that the cannon does not experience any recoil in the horizontal direction.