Final answer:
Using the kinetic energy formula and rearranging it to solve for velocity, the 0.50 kg ball with kinetic energy of 400 J is moving at a speed of 40 m/s.
Step-by-step explanation:
To find out how fast a 0.50 kg ball is moving if its kinetic energy is 400 J, we need to use the kinetic energy formula: K = 1/2mv², where K is the kinetic energy, m is the mass of the object, and v is the velocity of the object. By rearranging the formula to solve for v, we get v = √(2K/m). Plugging in the values, we get v = √(2×400 J / 0.50 kg), which equals v = √(800 J / 0.50 kg) leading to v = √(1600), so the velocity is 40 m/s.