How far did the second ball fall if a person throws it downward with an initial velocity of 3 m/s, and both balls hit the ground at the same time from a height of 10 m?

To determine how far the second ball fell when thrown downward with an initial velocity of 3 m/s from a height of 10 meters, we can apply the principles of kinematics.

First, we need to calculate the time it takes for the first ball (dropped with zero initial velocity) to reach the ground. Using the equation for free fall:

[ d = \frac{1}{2} g t^2 ]

where d is the distance fallen (10 m), g is the acceleration due to gravity (approximately 9.81 m/s²), and t is the time in seconds. Rearranging the formula to solve for time gives:

[ t = \sqrt{\frac{2d}{g}} ]

Substituting the known values:

[ t = \sqrt{\frac{2 \times 10 \text{ m}}{9.81 \text{ m/s}^2}} \approx \sqrt{2.04} \approx 1.43 \text{ seconds} ]

Now that we know the time it takes for the first ball to fall, we can calculate how far the second ball falls in the same amount of time, considering it has an initial downward velocity of 3