Final answer:
The horizontal component of a cannonball's velocity remains constant throughout its flight in the absence of air resistance, due to the lack of horizontal forces. In the circus act scenario, the performer's recoil velocity is calculated using conservation of momentum, where the initial momentum of the cannonball equals the final momentum of the performer and the cannonball together.
Step-by-step explanation:
The question you've asked involves the principles of projectile motion, particularly focusing on the horizontal component of the cannonball's velocity. When a projectile is fired on Earth and air resistance can be ignored, the horizontal component of its velocity remains constant throughout its flight. This is because there's no acceleration acting in the horizontal direction once the projectile is in motion, assuming no air resistance. Gravity acts downwards and only affects the vertical component of the motion.
To address the question from the circus act scenario, we can use the conservation of momentum principle to find the performer's recoil velocity. Before the performer catches the cannonball, the momentum of the system is just the momentum of the cannonball since the performer is initially at rest. For the system, the total momentum before the catch must equal the total momentum after the catch, because momentum is conserved in the absence of external forces.
The initial momentum of the system (pi) is just the momentum of the cannonball, which is its mass (10.0 kg) multiplied by its horizontal velocity (8.00 m/s). The final momentum of the system (pf) is the combined mass of the performer and the cannonball, moving together at the recoil velocity (v). So, pi = pf, or (10.0 kg)(8.00 m/s) = (10.0 kg + 65.0 kg)(v). Solving for v gives us the recoil velocity.