Final answer:
In the circus act, the correct equation describing the system after the cannon is fired is momentum of the cannon + momentum of human = 0, which is based on the conservation of momentum in closed systems.
Step-by-step explanation:
In a circus act, a 100 kg "human cannonball" is fired from a 400 kg cannon on wheels. After the cannon is fired, the equation c) momentum of the cannon + momentum of human = 0 describes the system because of the conservation of momentum.
This principle states that in the absence of external forces, the total momentum of a system remains constant. In the given scenario, the system involves the cannon and the human cannonball. Since the cannonball is fired forward, the cannon must recoil backward to conserve the total momentum of the system. The momentum before the event (with both the cannon and human cannonball at rest) is zero, so the momentum after must also sum to zero.
Example Calculation: Using the conservation of momentum concept, let's consider a scenario where an elderly performer catches a cannon ball. The cannon ball has a mass of 10.0 kg and the horizontal component of its velocity is 8.00 m/s. If the performer has a mass of 65.0 kg and is on nearly frictionless roller skates, we can use the conservation of momentum to calculate his recoil velocity. The combined momentum before the catch is 80 kg·m/s (10.0 kg × 8.00 m/s) and must be equal to the total momentum after the performer catches the cannon ball.
Accordingly, the formula for the recoil velocity v of the performer is (10.0 kg × 8.00 m/s) = (65.0 kg + 10.0 kg) × v, solving for v gives us the performer's recoil velocity. This problem relates to the principles of linear momentum and conservation laws in classical mechanics.