A bomb is dropped from an aeroplane flying horizontally with a velocity of 720 kmph at an altitude of 980m. Time taken by the bomb to hit the ground is

Options

A. 1s
B. 7.2 s
C. 14.14 s
D. 0.15 s

Explanation

To solve the problem of finding the time taken by a bomb to hit the ground when dropped from an airplane flying horizontally, we can follow these steps:

### Step 1: Understand the problem
The bomb is dropped from an airplane at an altitude of 980 meters. The airplane is flying horizontally at a speed of 720 km/h. We need to determine how long it takes for the bomb to fall to the ground.

### Step 2: Convert the speed of the airplane
First, we need to convert the speed of the airplane from kilometers per hour (km/h) to meters per second (m/s).

\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \]

Substituting the given speed:

\[ \text{Speed} = 720 \times \frac{5}{18} = 200 \text{ m/s} \]

### Step 3: Use the formula for time of flight
The time taken for the bomb to hit the ground can be calculated using the formula for the time of flight for an object in free fall:

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

Where:
- \( h \) is the height (980 m)
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \))

### Step 4: Substitute the values into the formula
Now, substituting the values into the formula:

\[ t = \sqrt{\frac{2 \times 980}{9.8}} \]

Calculating the value inside the square root:

\[ t = \sqrt{\frac{1960}{9.8}} = \sqrt{200} \]

### Step 5: Calculate the square root
Now, we calculate the square root of 200:

\[ t \approx 14.14 \text{ seconds} \]

### Final Answer
The time taken by the bomb to hit the ground is approximately **14.14 seconds**.

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