Final answer:
The ball with 80 J of kinetic energy and a mass of 2 kg is rolling at a speed of 6.32 meters per second.
Step-by-step explanation:
To determine how fast a ball is rolling with a given kinetic energy, we can use the formula for kinetic energy (KE): KE = 1/2 m v², where m is the mass and v is the velocity. Given that the ball has 80 J of kinetic energy and a mass of 2 kg, we rearrange the formula to solve for velocity: v = sqrt(2KE/m).
Now we plug in the values: v = sqrt(2*80 J / 2 kg) = sqrt(160 J / 2 kg) = sqrt(80 kg*m²/s² / 2 kg) = sqrt(40 m²/s²) = 6.32 m/s. Therefore, the ball is rolling at 6.32 meters per second.