An NCC parade is going at a uniform speed of 6 km/h thorugh a place under a berry tree on which a bird is sitting at a height of 12.1 m. At a particular instant the bird drops a berry. Which cadet (gie the distance from the tree at tehinstant) will receive the berry on his uniform?

Explanation

To solve the problem step by step, we need to determine the time it takes for the berry to fall from the height of 12.1 meters and then calculate how far the NCC parade travels during that time.

### Step 1: Calculate the time taken for the berry to fall
The formula for the distance fallen under gravity is given by:
\[ S = ut + \frac{1}{2}gt^2 \]
Where:
- \( S \) = distance fallen (12.1 m)
- \( u \) = initial velocity (0 m/s, since the berry is dropped)
- \( g \) = acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \))
- \( t \) = time in seconds

Since the initial velocity \( u = 0 \), the equation simplifies to:
\[ S = \frac{1}{2}gt^2 \]

Substituting the known values:
\[ 12.1 = \frac{1}{2} \times 9.8 \times t^2 \]
\[ 12.1 = 4.9t^2 \]

Now, solving for \( t^2 \):
\[ t^2 = \frac{12.1}{4.9} \]
\[ t^2 = 2.463 \]
\[ t = \sqrt{2.463} \]
\[ t \approx 1.57 \, \text{seconds} \]

### Step 2: Convert the speed of the NCC parade into meters per second
The speed of the NCC parade is given as 6 km/h. To convert this to meters per second:
\[ \text{Speed} = 6 \, \text{km/h} = \frac{6 \times 1000 \, \text{m}}{3600 \, \text{s}} \]
\[ \text{Speed} = \frac{6000}{3600} \]
\[ \text{Speed} = \frac{5}{3} \, \text{m/s} \]

### Step 3: Calculate the distance traveled by the parade during the time the berry falls
Now we can calculate the distance \( d \) that the parade travels while the berry is falling:
\[ d = \text{Speed} \times t \]
\[ d = \left(\frac{5}{3} \, \text{m/s}\right) \times (1.57 \, \text{s}) \]
\[ d \approx \frac{5 \times 1.57}{3} \]
\[ d \approx \frac{7.85}{3} \]
\[ d \approx 2.62 \, \text{meters} \]

### Conclusion
The cadet who will receive the berry on his uniform is approximately **2.62 meters** away from the tree at the instant the berry is dropped.

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