Final answer:
To calculate the velocity of a falling ball from a certain height, one should use the equation (1/2)mv² = mgΔh and rearrange it to solve for 'v', resulting in v = (2gΔh)¹/².
Step-by-step explanation:
To find the velocity of a ball after it has fallen through a certain distance, you could rearrange the equality representing the conservation of mechanical energy. The correct equality for this scenario is (1/2)mv² = mgΔh, where 'm' represents the mass of the ball, 'v' is its velocity at the impact, 'g' is the acceleration due to gravity, and 'Δh' is the change in height from the point of drop to the point of impact. From this equation, solving for 'v' can give us the velocity of the ball.
Specifically, if you rearrange the equation to solve for 'v', it will look like this: v = (2gΔh)¹/². Keep in mind that in this case, air resistance is being ignored, and it's assumed that the ball is falling in a vacuum or air resistance is negligible.