A storne is dropped from the `25` th storey of a multistored building and it reaches the ground in `5 s`. In the first second, it passes through how many storey of the buliding?

Options

A. `1`
B. `2`
C. `3`
D. none of ther

Explanation

To solve the problem step by step, we will determine how many stories the stone crosses in the first second after being dropped from the 25th story of a building.

### Step 1: Understand the problem
The stone is dropped from the 25th story and takes 5 seconds to reach the ground. We need to find out how many stories it crosses in the first second.

### Step 2: Define the height of each story
Let the height of each story be denoted as \( H \). Since the stone is dropped from the 25th story, the total height of the building can be expressed as:
\[ \text{Total height} = 25H \]

### Step 3: Use the second equation of motion
Since the stone is dropped (initial velocity \( u = 0 \)), we can use the second equation of motion to find the total height it falls in 5 seconds:
\[ s = ut + \frac{1}{2}gt^2 \]
Substituting \( u = 0 \), \( g = 10 \, \text{m/s}^2 \) (approximately), and \( t = 5 \, \text{s} \):
\[ s = 0 + \frac{1}{2} \cdot 10 \cdot (5^2) = \frac{1}{2} \cdot 10 \cdot 25 = 125 \, \text{m} \]
So, the total height of the building is:
\[ 25H = 125 \implies H = 5 \, \text{m} \]

### Step 4: Calculate the distance fallen in the first second
To find out how far the stone falls in the first second, we can use the formula for the distance covered in the nth second:
\[ S_n = u + \frac{a}{2} \cdot (2n - 1) \]
For the first second (\( n = 1 \)):
\[ S_1 = 0 + \frac{10}{2} \cdot (2 \cdot 1 - 1) = 5 \cdot 1 = 5 \, \text{m} \]

### Step 5: Determine how many stories are crossed
Since each story has a height of \( H = 5 \, \text{m} \), the number of stories crossed in the first second is:
\[ \text{Number of stories crossed} = \frac{S_1}{H} = \frac{5 \, \text{m}}{5 \, \text{m}} = 1 \]

### Final Answer
The stone crosses **1 story** in the first second.