Water stands at a depth `H` in a tank whose side walls are vertical. A hole is made on one of the walls at a depth `h` below the water surface. Find at what distance from the foot of the wall does the emerging stream of water strike the floor and for what value of `h` this range is maximum ? What is the maximum possible range ?

Explanation

To solve the problem, we need to determine the distance from the foot of the wall where the emerging stream of water strikes the floor and find the value of \( h \) that maximizes this distance.

### Step-by-step Solution:

1. **Determine the velocity of the water at the hole:**
The velocity of the water emerging from the hole can be calculated using Torricelli's theorem, which states that the speed \( V \) of efflux of a fluid under the force of gravity through an orifice is given by:
\[
V = \sqrt{2g(H - h)}
...