An aeroplane flying horizontally with a speed of 360 km `h^(-1)` releases a bomb at a height of 490 m from the ground. If g = 9. 8 m `s^(-2)` , it will strike the ground at

Options

A. 10 km
B. 100 km
C. 1 km
D. 16 km

Explanation

To solve the problem of determining how far the bomb will strike the ground after being released from the airplane, we can follow these steps:

### Step 1: Convert the speed of the airplane from km/h to m/s
The speed of the airplane is given as 360 km/h. To convert this to meters per second (m/s), we use the conversion factor:

\[ 1 \text{ km/h} = \frac{1}{3.6} \text{ m/s} \]

Thus,

\[ \text{Speed in m/s} = 360 \times \frac{1}{3.6} = 100 \text{ m/s} \]

### Step 2: Calculate the time taken for the bomb to fall to the ground
The bomb is released from a height of 490 m. We can use the equation of motion for free fall to find the time taken (t) to hit the ground:

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

Where:
- \( h = 490 \text{ m} \)
- \( g = 9.8 \text{ m/s}^2 \)

Rearranging the equation to solve for \( t \):

\[ t^2 = \frac{2h}{g} = \frac{2 \times 490}{9.8} \]

Calculating this gives:

\[ t^2 = \frac{980}{9.8} = 100 \implies t = \sqrt{100} = 10 \text{ seconds} \]

### Step 3: Calculate the horizontal distance traveled by the bomb
The horizontal distance (range) can be calculated using the formula:

\[ \text{Range} = \text{Speed} \times \text{Time} \]

Substituting the values we have:

\[ \text{Range} = 100 \text{ m/s} \times 10 \text{ s} = 1000 \text{ m} \]

### Step 4: Convert the distance from meters to kilometers
Since the question asks for the distance in kilometers:

\[ 1000 \text{ m} = 1 \text{ km} \]

### Final Answer
The bomb will strike the ground at a distance of **1 kilometer** from the point directly below where it was released.

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