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, we will follow these steps:

### Step 1: Understand the problem
A stone is dropped from the 25th storey of a building and takes 5 seconds to reach the ground. We need to find out how many storeys the stone passes through in the first second.

### Step 2: Define the variables
Let:
- \( h \) = height of each storey (unknown)
- \( n \) = number of storeys (25 in this case)
- \( g \) = acceleration due to gravity = \( 10 \, \text{m/s}^2 \)
- \( t \) = total time taken to reach the ground = 5 seconds

### Step 3: Calculate the total height of the building
The total height \( H \) of the building can be expressed as:
\[ H = n \cdot h = 25h \]
Using the second equation of motion for the stone dropped from rest:
\[ H = ut + \frac{1}{2} g t^2 \]
Since the initial velocity \( u = 0 \) (the stone is dropped), we have:
\[ H = 0 + \frac{1}{2} \cdot 10 \cdot (5^2) \]
\[ H = \frac{1}{2} \cdot 10 \cdot 25 = 125 \, \text{meters} \]

### Step 4: Find the height of each storey
Now, we can find the height of each storey \( h \):
\[ 25h = 125 \implies h = \frac{125}{25} = 5 \, \text{meters} \]

### Step 5: Calculate the displacement in the first second
To find out how many storeys the stone passes through in the first second, we can use the formula for displacement in the first second:
\[ s_1 = ut + \frac{1}{2} g t^2 \]
For the first second (\( t = 1 \)):
\[ s_1 = 0 + \frac{1}{2} \cdot 10 \cdot (1^2) = \frac{1}{2} \cdot 10 \cdot 1 = 5 \, \text{meters} \]

### Step 6: Determine how many storeys are passed
Since each storey is 5 meters high, the number of storeys passed in the first second is:
\[ \text{Number of storeys} = \frac{s_1}{h} = \frac{5}{5} = 1 \]

### Final Answer
The stone passes through **1 storey** in the first second.

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