A jet aeroplane is flying at a constant height of 2 km with a speed `360 kmh^(-1)` above the ground towards a target and releases a bomb. After how much time it will hit the target and what will be the horizontal distance of the aeroplane from the target so that the bomb should hit the target ? (Take `g = 10 ms^(-2))`

Options

A. 10s, 1km
B. 20 s, 2km
C. 30s, 3km
D. 40s, 4km

Explanation

To solve the problem step by step, we will break it down into two parts: calculating the time it takes for the bomb to hit the target and then determining the horizontal distance from the aeroplane to the target.

### Step 1: Convert the speed of the aeroplane from km/h to m/s
The speed of the aeroplane is given as 360 km/h. We need to convert this to meters per second (m/s).

\[ \text{Speed in m/s} = \frac{360 \text{ km}}{1 \text{ h}} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{3600 \text{ s}} = \frac{360 \times 1000}{3600} = 100 \text{ m/s} \]

### Step 2: Calculate the time taken for the bomb to hit the ground
The bomb is released from a height of 2 km (2000 m). We will use the second equation of motion to find the time taken for the bomb to fall to the ground.

The equation is:
\[ s = ut + \frac{1}{2} a t^2 \]
Where:
- \(s = 2000 \text{ m}\) (the height)
- \(u = 0 \text{ m/s}\) (initial vertical velocity)
- \(a = g = 10 \text{ m/s}^2\) (acceleration due to gravity)

Substituting the values into the equation:
\[ 2000 = 0 \cdot t + \frac{1}{2} \cdot 10 \cdot t^2 \]
This simplifies to:
\[ 2000 = 5t^2 \]
\[ t^2 = \frac{2000}{5} = 400 \]
\[ t = \sqrt{400} = 20 \text{ seconds} \]

### Step 3: Calculate the horizontal distance from the aeroplane to the target
Now that we have the time, we can find the horizontal distance using the formula:
\[ \text{Horizontal Distance} = \text{Horizontal Velocity} \times \text{Time} \]
Where:
- Horizontal Velocity \(v_x = 100 \text{ m/s}\)
- Time \(t = 20 \text{ seconds}\)

Substituting the values:
\[ \text{Horizontal Distance} = 100 \text{ m/s} \times 20 \text{ s} = 2000 \text{ m} = 2 \text{ km} \]

### Final Results
- The time taken for the bomb to hit the target is **20 seconds**.
- The horizontal distance from the aeroplane to the target is **2 km**.