To estimate the height of a bridge over a river, a stone is dropped freely on the river from the bridge. The stone takes 2 s to touch the water surface in the river. Calculate the height of the bridge from the water level. Take `g=9.8m//s^(2)`

Explanation

To calculate the height of the bridge from which the stone is dropped, we can use the second equation of motion, which relates the distance traveled by an object under uniform acceleration to its initial velocity, time, and acceleration due to gravity.

### Step-by-Step Solution:

1. **Identify the known values:**
- Initial velocity (u) = 0 m/s (since the stone is dropped)
- Time (t) = 2 s (the time taken for the stone to reach the water)
- Acceleration due to gravity (g) = 9.8 m/s²

2. **Use the second equation of motion:**
The second equation of motion states:
\[ S = ut + \frac{1}{2} g t^2 \]
where:
- S is the distance traveled (height of the bridge, h in this case)
- u is the initial velocity
- g is the acceleration due to gravity
- t is the time taken

3. **Substitute the known values into the equation:**
Since the initial velocity (u) is 0, the equation simplifies to:
\[ h = 0 \cdot t + \frac{1}{2} g t^2 \]
This simplifies to:
\[ h = \frac{1}{2} g t^2 \]

4. **Calculate \( t^2 \):**
\[ t^2 = (2 \, \text{s})^2 = 4 \, \text{s}^2 \]

5. **Substitute \( g \) and \( t^2 \) into the equation:**
\[ h = \frac{1}{2} \cdot 9.8 \, \text{m/s}^2 \cdot 4 \, \text{s}^2 \]

6. **Calculate \( h \):**
\[ h = \frac{1}{2} \cdot 9.8 \cdot 4 = 19.6 \, \text{m} \]

### Final Answer:
The height of the bridge from the water level is **19.6 meters**.