Understanding the Physics

* Gravity: The ball will be affected by gravity, causing it to slow down as it goes up and speed up as it comes back down.

* Symmetry: The time it takes for the ball to reach its highest point is the same as the time it takes to fall back down to the height it was thrown from.

Setting up the Problem

* Initial velocity (u): 20 m/s (upwards)

* Acceleration due to gravity (g): -9.8 m/s² (downwards)

* Displacement (s): 0 meters (since the ball needs to pass the man's position again)

Using a Kinematic Equation

We can use the following kinematic equation to find the time (t):

s = ut + (1/2)gt²

Solving for Time (t)

1. Plug in the values:

0 = 20t + (1/2)(-9.8)t²

0 = 20t - 4.9t²

2. Rearrange the equation:

4.9t² - 20t = 0

3. Factor out t:

t(4.9t - 20) = 0

4. Solve for t:

* t = 0 (This represents the initial moment the ball was thrown)

* 4.9t - 20 = 0 => t = 20 / 4.9 ≈ 4.08 seconds

Answer

The ball will pass the man again after approximately 4.08 seconds.