Analysis:
To find the time taken for the ball to hit the ground, we need to consider the motion of the ball in two parts: the upward motion and the downward motion.

Upward Motion:
During the upward motion, the ball experiences a constant acceleration due to gravity, which is equal to -9.8 m/s^2. The initial velocity of the ball is V, and the final velocity at the peak of its motion is 0. We can use the equation of motion to find the time taken for the upward motion:

V = u + at

Since the final velocity is 0, we have:

0 = V - 9.8t

Solving for t, we get:

t = V/9.8

Downward Motion:
During the downward motion, the ball falls freely under gravity. The initial height of the ball above the ground is H. We can use the equation of motion to find the time taken for the downward motion:

H = ut + (1/2)at^2

Since the initial velocity is 0 and the acceleration is -9.8 m/s^2, we have:

H = 0 + (1/2)(-9.8)t^2

Simplifying the equation, we get:

H = -4.9t^2

Solving for t, we get:

t = sqrt(H/4.9)

Total Time:
The total time taken for the ball to hit the ground is the sum of the time taken for the upward and downward motions:

Total time = t (upward) + t (downward)

Substituting the values of t (upward) and t (downward), we get:

Total time = V/9.8 + sqrt(H/4.9)

Example:
Let's consider an example where the initial velocity of the ball is 10 m/s and the height above the ground is 20 m.

Using the equations derived above, we can calculate the total time taken for the ball to hit the ground:

Total time = 10/9.8 + sqrt(20/4.9)
= 1.02 + 1.43
= 2.45 seconds

Therefore, in this example, it would take approximately 2.45 seconds for the ball to hit the ground.

Note:
Please note that this analysis assumes that there is no air resistance and neglects any other factors that may affect the motion of the ball.