A bomber aeroplane is flying horizontally at a height of 12250 metres with a velocity `800 km//"hour"`. It has to drop a bomb on a target on the ground. How far, horizontally, should the bomber be from the target when the bomb should be dropped? How much time the bomb takes to reach the target ? Take `g=9.8 m//"sec"^(2)`

Answer

To solve the problem of how far horizontally the bomber should be from the target when the bomb is dropped, we will follow these steps:

### Step 1: Convert the velocity from km/h to m/s
The velocity of the bomber is given as 800 km/h. We need to convert this to meters per second (m/s) using the conversion factor \(1 \text{ km/h} = \frac{1}{3.6} \text{ m/s}\).

\[ \text{Velocity in m/s} = 800 \, \text{km/h} \times \frac{1 \, \text{m/s}}{3.6 \, \text{km/h}} = \frac{800}{3.6} \approx 222.22 \, \text{m/s} \]

### Step 2: Calculate the time taken for the bomb to fall to the ground
The height from which the bomb is dropped is 12250 meters. We can use the formula for the time of free fall under gravity:

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

Rearranging this gives:

\[ t^2 = \frac{2h}{g} \]

Substituting the values \(h = 12250 \, \text{m}\) and \(g = 9.8 \, \text{m/s}^2\):

\[ t^2 = \frac{2 \times 12250}{9.8} \approx \frac{24500}{9.8} \approx 2500 \]

Taking the square root:

\[ t = \sqrt{2500} = 50 \, \text{s} \]

### Step 3: Calculate the horizontal distance the bomb travels
Now that we have the time taken for the bomb to reach the ground, we can calculate the horizontal distance using the formula:

\[ \text{Distance} = \text{Velocity} \times \text{Time} \]

Substituting the values:

\[ \text{Distance} = 222.22 \, \text{m/s} \times 50 \, \text{s} \approx 11111 \, \text{m} \]

### Final Answers
- The bomber should be approximately **11111 meters** away from the target when the bomb is dropped.
- The bomb takes **50 seconds** to reach the target.