Understanding the Physics

* Gravity: The primary force acting on the ball is gravity, which pulls it downward at an acceleration of approximately 9.8 m/s².

* 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 back down.

Calculations

1. Find the time to reach the highest point:

* At the highest point, the ball's velocity is 0 m/s.

* Use the following kinematic equation:

* v = u + at (where:

* v = final velocity (0 m/s)

* u = initial velocity (20 m/s)

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

* t = time)

* Solving for t:

* 0 = 20 - 9.8t

* t = 20 / 9.8 ≈ 2.04 seconds

2. Total time: Since the upward and downward times are equal, the total time for the ball to return to your hand is:

* 2.04 seconds (up) + 2.04 seconds (down) = 4.08 seconds

Therefore, the ball will return to your hand after approximately 4.08 seconds.