A stone dropped from a building takes 4 s to reach the ground. The height of the building is

Options

A. `19.6m`
B. `80.4m`
C. `78.4m`
D. `156.8m`

Explanation

To find the height of the building from which a stone is dropped, we can use the equations of motion under uniform acceleration due to gravity. Here’s a step-by-step solution:

### Step 1: Identify the known values
- Time taken (t) = 4 seconds
- Initial velocity (u) = 0 m/s (since the stone is dropped)
- Acceleration due to gravity (g) = 9.8 m/s² (approximately)

### Step 2: Use the equation of motion
We will use the second equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]
where:
- \( s \) is the distance (height of the building, H)
- \( u \) is the initial velocity
- \( a \) is the acceleration (which is g in this case)
- \( t \) is the time taken

### Step 3: Substitute the known values into the equation
Since the initial velocity \( u = 0 \), the equation simplifies to:
\[ H = 0 \cdot t + \frac{1}{2} g t^2 \]
Substituting the values:
\[ H = \frac{1}{2} \cdot 9.8 \cdot (4)^2 \]

### Step 4: Calculate \( H \)
Calculating \( (4)^2 \):
\[ (4)^2 = 16 \]
Now substituting back:
\[ H = \frac{1}{2} \cdot 9.8 \cdot 16 \]
Calculating \( \frac{1}{2} \cdot 9.8 = 4.9 \):
\[ H = 4.9 \cdot 16 \]
Now calculating \( 4.9 \cdot 16 \):
\[ H = 78.4 \text{ meters} \]

### Final Answer
The height of the building is **78.4 meters**.

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