An acroplane is flying horizontally with a velocity of 600 km/h and a height of 1960m. When it is vectrically above a point A on the ground a bomb is released from it. The bomb strikes the ground at point B. the distance AB is:

Options

A. 3.33 km
B. 333 km
C. 33.3 km
D. 3330

Explanation

To solve the problem of finding the distance \( AB \) where a bomb released from an airplane strikes the ground, we can follow these steps:

### Step-by-Step Solution:

1. **Convert the velocity of the airplane from km/h to m/s**:
\[ \text{Velocity} = 600 \text{ km/h} = \frac{600 \times 1000}{3600} \text{ m/s} = \frac{600 \times 1000}{3600} = \frac{500}{3} \text{ m/s} \]

2. **Determine the time taken for the bomb to fall from the height of 1960 m**:
We can use the second equation of motion:
\[ h = \frac{1}{2} g t^2 \]
where \( h = 1960 \) m and \( g \approx 9.8 \text{ m/s}^2 \).
Rearranging the equation gives:
\[ t^2 = \frac{2h}{g} = \frac{2 \times 1960}{9.8} \]
Calculating this:
\[ t^2 = \frac{3920}{9.8} \approx 400 \implies t = \sqrt{400} = 20 \text{ seconds} \]

3. **Calculate the horizontal distance \( AB \)**:
The horizontal distance can be calculated using:
\[ \text{Distance} = \text{Velocity} \times \text{Time} \]
Substituting the values we have:
\[ AB = \left(\frac{500}{3}\right) \times 20 = \frac{10000}{3} \text{ meters} \]

4. **Convert the distance from meters to kilometers**:
\[ AB = \frac{10000}{3} \text{ m} = \frac{10000}{3000} \text{ km} \approx 3.33 \text{ km} \]

### Final Answer:
The distance \( AB \) is approximately \( 3.33 \) kilometers.

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