Understanding the Physics

* Symmetry: The upward and downward paths of the ball are symmetrical. This means the time it takes to go up is equal to the time it takes to come down.

* Acceleration due to gravity: The ball experiences a constant acceleration due to gravity (approximately 9.8 m/s²) acting downwards.

Calculations

1. Time for one way: Since the total time in the air is 6.16 seconds, the time for the ball to travel up (or down) is half that:

6.16 s / 2 = 3.08 s

2. Initial Velocity: We can use the following kinematic equation to find the initial velocity (v₀) of the ball:

* v = v₀ + at

Where:

* v = final velocity (0 m/s at the highest point)

* v₀ = initial velocity (what we want to find)

* a = acceleration due to gravity (-9.8 m/s²)

* t = time to reach the highest point (3.08 s)

* 0 = v₀ + (-9.8 m/s²) * 3.08 s

* v₀ = 30.18 m/s

3. Maximum Height: We can use another kinematic equation to find the maximum height (h) the ball reaches:

* h = v₀t + (1/2)at²

* h = (30.18 m/s) * (3.08 s) + (1/2) * (-9.8 m/s²) * (3.08 s)²

* h = 46.5 m (approximately)

Therefore:

* The initial velocity of the softball was approximately 30.18 m/s.

* The maximum height the softball reached was approximately 46.5 meters.