Final answer:
Using the conservation of momentum and the given values for the mass and velocity of the person, the mass of the steel ball was calculated as approximately 20.14 kg, therefore the correct answer is C. 20.14 kg.
Step-by-step explanation:
The problem involves the conservation of momentum, which states that the initial momentum of an isolated system is equal to the final momentum when no external forces act on it. The person and the steel ball system is initially at rest which means the initial momentum is zero.
To find the mass of the steel ball, we use the formula for momentum (p) which is the product of mass (m) and velocity (v): p = m * v. For two objects moving in opposite directions after an event, their momenta are related by m1 * v1 = m2 * v2 because the initial momentum of the system (person plus steel ball) is zero.
Let mperson be the mass of the person, vperson be the velocity of the person, mball be the mass of the steel ball, and vball be the velocity of the steel ball. Using the given values: mperson = 65.25 kg, vperson = 1.25 m/s to the right and vball = 4.05 m/s to the left, we can rearrange the equation to solve for mball: mperson * vperson = mball * vball.
Therefore, the mass of the steel ball is mball = (65.25 kg * 1.25 m/s) / 4.05 m/s, which equals approximately 20.14 kg.
The correct answer is C. 20.14 kg.