Final answer:
Using the kinetic energy formula KE = ½ mv², and rearranging it to solve for mass as m = 2KE/v², the mass of a rolling ball with 2,819 J of energy and rolling at a velocity of 61 m/s is calculated to be approximately 1.51 kg.
Step-by-step explanation:
To determine the mass of a rolling ball given its kinetic energy and velocity, we can use the kinetic energy formula KE = ½ mv², where KE is kinetic energy, m is mass, and v is velocity. From the question, we are given a kinetic energy of 2,819 J and a velocity of 61 m/s.
First, we rearrange the formula to solve for mass (m): m = 2KE/v²
Plugging in the values: m = 2 * 2,819 J / (61 m/s)²
m = 5,638 J / (61 m/s)²
m = 5,638 J / 3,721 m²/s²
m ≈ 1.51 kg
Therefore, the mass of the rolling ball is approximately 1.51 kilograms.