Final answer:
To find the performer's recoil velocity, the conservation of momentum equation is used, setting the initial momentum of the cannon ball equal to the final momentum of the performer and the ball together. After calculations, the recoil velocity of the performer is determined to be 1.067 m/s.
Step-by-step explanation:
The situation described involves the principle of conservation of momentum, which is a fundamental concept in physics. First, we need to understand that the total momentum of a closed system is constant if no external forces act on it. In this case, the circus performer and the cannon ball create a closed system.
To find the performer's recoil velocity, we set the momentum of the cannon ball before it is caught equal to the combined momentum of the performer and the cannon ball after the catch, as there are no external horizontal forces acting on the system. The equation for this scenario is:
mcannon ballvcannon ball = (mperformer + mcannon ball)vrecoil
Plugging in the given values:
10.0 kg * 8.00 m/s = (65.0 kg + 10.0 kg)vrecoil
Solving for vrecoil:
vrecoil = (10.0 kg * 8.00 m/s) / (65.0 kg + 10.0 kg)
vrecoil = 80.0 kg*m/s / 75.0 kg
vrecoil = 1.067 m/s
Therefore, the performer's recoil velocity is 1.067 m/s in the same direction as the cannon ball's initial velocity.