A stone rolls off the roof of a School hall and falls vartically. Just before it reaches the ground, the stone's speed is 17 m/s. Neglect air resistance and determine the height of the School Hall.

Options

A. 42m
B. 33m
C. 26m
D. 15m

Answer

To determine the height of the School Hall from which the stone falls, we can use the kinematic equation that relates the final velocity, initial velocity, acceleration, and displacement (height in this case). The equation is:

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

Where:
- \( v \) = final velocity (17 m/s)
- \( u \) = initial velocity (0 m/s, since the stone starts from rest)
- \( a \) = acceleration due to gravity (approximately \( 10 \, \text{m/s}^2 \))
- \( s \) = height (which we need to find)

### Step 1: Identify the known values
- Final velocity \( v = 17 \, \text{m/s} \)
- Initial velocity \( u = 0 \, \text{m/s} \)
- Acceleration \( a = 10 \, \text{m/s}^2 \)

### Step 2: Substitute the known values into the equation
Using the kinematic equation:

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

Substituting the known values:

\[ (17)^2 = (0)^2 + 2 \cdot (10) \cdot h \]

### Step 3: Calculate \( v^2 \)
Calculating \( 17^2 \):

\[ 289 = 0 + 20h \]

### Step 4: Solve for \( h \)
Now, we can solve for \( h \):

\[ 289 = 20h \]

Dividing both sides by 20:

\[ h = \frac{289}{20} \]

### Step 5: Calculate the height
Calculating \( h \):

\[ h = 14.45 \, \text{m} \]

Thus, the height of the School Hall is approximately \( 14.45 \, \text{m} \).

### Final Answer:
The height of the School Hall is approximately **14.45 meters**.

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