A freely falling body covers _____ of total distance in 3rd second.

Options

A. `8%`
B. `35.5%`
C. `55.55%`
D. `45.5%`

Answer

To solve the problem of finding the distance covered by a freely falling body in the third second, we can follow these steps:

### Step 1: Identify the parameters
- For a freely falling body:
- Initial velocity (u) = 0 m/s (since it starts from rest)
- Acceleration (a) = 10 m/s² (acceleration due to gravity)

### Step 2: Use the formula for distance covered in the nth second
The formula to calculate the distance covered in the nth second is given by:
\[ d_n = u + \frac{a}{2} \cdot (2n - 1) \]
Where:
- \(d_n\) = distance covered in the nth second
- \(u\) = initial velocity
- \(a\) = acceleration
- \(n\) = the second in which we want to find the distance

### Step 3: Substitute the values for the third second (n = 3)
Substituting \(u = 0\), \(a = 10\), and \(n = 3\):
\[ d_3 = 0 + \frac{10}{2} \cdot (2 \cdot 3 - 1) \]
\[ d_3 = 5 \cdot (6 - 1) \]
\[ d_3 = 5 \cdot 5 = 25 \text{ meters} \]

### Step 4: Calculate the total distance covered in 3 seconds
To find the total distance covered in the first 3 seconds, we can use the second equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]
Substituting \(u = 0\), \(a = 10\), and \(t = 3\):
\[ s = 0 + \frac{1}{2} \cdot 10 \cdot (3^2) \]
\[ s = 5 \cdot 9 = 45 \text{ meters} \]

### Step 5: Calculate the percentage of distance covered in the 3rd second
To find the percentage of the total distance covered in the 3rd second:
\[ \text{Percentage} = \left( \frac{d_3}{s} \right) \cdot 100 \]
Substituting the values:
\[ \text{Percentage} = \left( \frac{25}{45} \right) \cdot 100 \]
\[ \text{Percentage} = \frac{5}{9} \cdot 100 \approx 55.56\% \]

### Final Answer
The body covers approximately **55.56%** of the total distance in the 3rd second.

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