A stone is thrown vertically up from a bridge with velocity `3 ms^(-1)`. If it strikes the water under the bridge after 2 s, the bridge is at a height of `(g = 10 "ms"^(-2) )`

Options

A. 26 m
B. 14 m
C. 7 m
D. 20 m

Answer

To solve the problem, we need to find the height of the bridge from which the stone is thrown. We will use the second equation of motion to determine the displacement of the stone after 2 seconds.

### Step-by-Step Solution:

1. **Identify the given values:**
- Initial velocity (u) = 3 m/s (upward)
- Acceleration (a) = -10 m/s² (downward, due to gravity)
- Time (t) = 2 s
- Displacement (s) = ? (this will be the height of the bridge)

2. **Use the second equation of motion:**
The second equation of motion states:
\[ s = ut + \frac{1}{2} a t^2 \]

3. **Substitute the known values into the equation:**
\[ s = (3 \, \text{m/s}) \times (2 \, \text{s}) + \frac{1}{2} \times (-10 \, \text{m/s}^2) \times (2 \, \text{s})^2 \]

4. **Calculate each term:**
- First term: \( 3 \times 2 = 6 \, \text{m} \)
- Second term:
\[ \frac{1}{2} \times (-10) \times (4) = -20 \, \text{m} \]

5. **Combine the results:**
\[ s = 6 \, \text{m} - 20 \, \text{m} = -14 \, \text{m} \]

6. **Interpret the result:**
The negative sign indicates that the stone has moved downward from the point of release to the water surface. Therefore, the height of the bridge is 14 meters.

### Final Answer:
The height of the bridge is **14 meters**.

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