An aeroplane moving horizontally with a speed of `720 km//h` drops a food pocket, while flying at a height of 396.9 m . the time taken by a food pocket to reach the ground and its horizontal range is (Take `g = 9.8 m//sec`)

Options

A. 3s and 2000m
B. 5s and 500 m
C. 8s and 1500m
D. 9s and 1800 m

Explanation

To solve the problem, we need to find two things: the time taken by the food packet to reach the ground and its horizontal range.

### Step 1: Calculate the time taken to reach the ground

We can use the formula for the distance fallen under gravity:

\[ s = ut + \frac{1}{2} g t^2 \]

Where:
- \( s \) is the distance fallen (396.9 m),
- \( u \) is the initial velocity (0 m/s, since the packet is dropped),
- \( g \) is the acceleration due to gravity (9.8 m/s²),
- \( t \) is the time taken to fall.

Since the initial velocity \( u = 0 \), the equation simplifies to:

\[ s = \frac{1}{2} g t^2 \]

Substituting the known values:

\[ 396.9 = \frac{1}{2} \times 9.8 \times t^2 \]

### Step 2: Rearranging the equation

To isolate \( t^2 \), we multiply both sides by 2:

\[ 2 \times 396.9 = 9.8 \times t^2 \]

This simplifies to:

\[ 793.8 = 9.8 \times t^2 \]

Now, divide both sides by 9.8:

\[ t^2 = \frac{793.8}{9.8} \]

### Step 3: Calculate \( t^2 \)

Calculating the right side:

\[ t^2 = 81 \]

### Step 4: Calculate \( t \)

Taking the square root of both sides gives:

\[ t = \sqrt{81} = 9 \text{ seconds} \]

### Step 5: Calculate the horizontal range

The horizontal range \( R \) can be calculated using the formula:

\[ R = u_x \times t \]

Where:
- \( u_x \) is the horizontal speed of the airplane,
- \( t \) is the time of flight.

The speed of the airplane is given as 720 km/h. We need to convert this to meters per second:

\[ u_x = 720 \text{ km/h} = \frac{720 \times 1000}{3600} = 200 \text{ m/s} \]

### Step 6: Calculate the horizontal range

Now substituting the values into the range formula:

\[ R = 200 \text{ m/s} \times 9 \text{ s} \]

Calculating this gives:

\[ R = 1800 \text{ m} \]

### Final Results

- Time taken by the food packet to reach the ground: **9 seconds**
- Horizontal range of the food packet: **1800 meters**

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