A stone is thrown downwards with velocity 10 m/s from the roof of a builng and it reaches the ground with speed 40 m/s. the height of the building would be

Options

A. 75 m
B. 100 m
C. 125 m
D. 150 m

Answer

To find the height of the building from which the stone is thrown downwards, we can use the kinematic equation:

\[ v^2 = u^2 + 2as \]

Where:
- \( v \) = final velocity (40 m/s)
- \( u \) = initial velocity (10 m/s)
- \( a \) = acceleration (which is \( g = 10 \, \text{m/s}^2 \) for downward motion)
- \( s \) = distance traveled (which is the height \( h \) of the building)

### Step-by-Step Solution:

1. **Identify the known values:**
- Initial velocity \( u = 10 \, \text{m/s} \)
- Final velocity \( v = 40 \, \text{m/s} \)
- Acceleration \( a = g = 10 \, \text{m/s}^2 \)

2. **Substitute the known values into the equation:**
\[ v^2 = u^2 + 2as \]
becomes
\[ (40)^2 = (10)^2 + 2 \cdot 10 \cdot h \]

3. **Calculate \( v^2 \) and \( u^2 \):**
\[ 1600 = 100 + 20h \]

4. **Rearranging the equation to solve for \( h \):**
\[ 1600 - 100 = 20h \]
\[ 1500 = 20h \]

5. **Divide both sides by 20:**
\[ h = \frac{1500}{20} = 75 \, \text{m} \]

6. **Conclusion:**
The height of the building is \( h = 75 \, \text{m} \).