A tank if filled with water upto height H. When a hole is made at a distance h below the level of water. What will be the horizontal range of water jet ?

Options

A. `2sqrt(h(H-h))`
B. `4sqrt(h(H+h))`
C. `4sqrt(h(H-h))`
D. `2sqrt(h(H+h))`

Explanation

To solve the problem of finding the horizontal range of the water jet when a hole is made in a tank filled with water, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
- We have a tank filled with water up to a height \( H \).
- A hole is made at a distance \( h \) below the water surface.

2. **Identify the Heights**:
- The height of water above the hole (which we will call \( h_{\text{top}} \)) is given by:
\[ h_{\text{top}} = H - h \]
- The height of the hole from the bottom of the tank (which we will call \( h_{\text{bottom}} \)) is simply:
\[ h_{\text{bottom}} = h \]

3. **Use the Range Formula**:
- The formula for the horizontal range \( R \) of a projectile (in this case, the water jet) is given by:
\[ R = 2 \sqrt{h_{\text{top}} \cdot h_{\text{bottom}}} \]
- Substituting the values of \( h_{\text{top}} \) and \( h_{\text{bottom}} \):
\[ R = 2 \sqrt{(H - h) \cdot h} \]

4. **Final Expression**:
- Therefore, the horizontal range of the water jet is:
\[ R = 2 \sqrt{(H - h) \cdot h} \]

### Final Answer:
The horizontal range of the water jet is given by:
\[ R = 2 \sqrt{(H - h) \cdot h} \]