A body is dropped from the roof of a multi storied building. It passes the ceiling of the 15th storey at a speed of `20 ms^(-1)`. If the height of each storey is 4m, the number of storeys in the building is `(take g = 10ms^(-2)` and neglect air resistance)

Options

A. 20
B. 25
C. 30
D. 35

Explanation

To solve the problem step by step, we need to analyze the motion of the body dropped from the roof of the building and determine the total number of storeys in the building.

### Step 1: Understand the given data
- The body is dropped from the roof of the building.
- It passes the ceiling of the 15th storey with a speed of \(20 \, \text{m/s}\).
- The height of each storey is \(4 \, \text{m}\).
- Acceleration due to gravity, \(g = 10 \, \text{m/s}^2\).

### Step 2: Use the kinematic equation
We can use the following kinematic equation to relate the final velocity, initial velocity, acceleration, and distance traveled:
\[ v^2 = u^2 + 2as \]
Where:
- \(v\) = final velocity = \(20 \, \text{m/s}\)
- \(u\) = initial velocity = \(0 \, \text{m/s}\) (since the body is dropped)
- \(a\) = acceleration = \(g = 10 \, \text{m/s}^2\)
- \(s\) = distance traveled (height from the roof to the ceiling of the 15th storey)

### Step 3: Substitute the values into the equation
Substituting the known values into the equation:
\[ (20)^2 = (0)^2 + 2 \cdot (10) \cdot s \]
\[ 400 = 20s \]

### Step 4: Solve for \(s\)
Now, we can solve for \(s\):
\[ s = \frac{400}{20} = 20 \, \text{m} \]

### Step 5: Calculate the number of storeys above the 15th storey
Since each storey is \(4 \, \text{m}\) high, we can find the number of storeys above the 15th storey:
\[ \text{Number of storeys above} = \frac{s}{\text{height of each storey}} = \frac{20 \, \text{m}}{4 \, \text{m/storey}} = 5 \, \text{storeys} \]

### Step 6: Calculate the total number of storeys in the building
The total number of storeys in the building is the number of storeys below the 15th storey plus the storeys above:
\[ \text{Total number of storeys} = 15 + 5 = 20 \]

### Final Answer
The total number of storeys in the building is **20**.

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