At the height 80 m , an aeroplane is moving with `150 m//s` . A bomb is dropped from it so as to hit a target. At what distance from the target should the bomb be dropped (given `g = 10 m//s`)

Options

A. `605.3m`
B. `600 m`
C. `80 m`
D. `230 m`

Answer

To solve the problem of determining at what distance from the target a bomb should be dropped from an airplane flying at a height of 80 m and a speed of 150 m/s, we can follow these steps:

### Step 1: Calculate the time taken for the bomb to fall
The bomb is dropped from a height of 80 m. We can use the equation of motion for free fall to find the time taken to reach the ground. The equation is given by:

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

Where:
- \( h = 80 \, \text{m} \) (height from which the bomb is dropped)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( t \) is the time in seconds.

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

\[ 80 = \frac{1}{2} \cdot 10 \cdot t^2 \]

\[ 80 = 5t^2 \]

\[ t^2 = \frac{80}{5} = 16 \]

\[ t = \sqrt{16} = 4 \, \text{s} \]

### Step 2: Calculate the horizontal distance traveled by the bomb
The bomb will continue to move horizontally at the same speed as the airplane when it is dropped. The horizontal distance \( d \) traveled by the bomb during the time \( t \) can be calculated using the formula:

\[ d = v \cdot t \]

Where:
- \( v = 150 \, \text{m/s} \) (horizontal speed of the airplane)
- \( t = 4 \, \text{s} \) (time calculated in Step 1)

Substituting the values:

\[ d = 150 \cdot 4 = 600 \, \text{m} \]

### Conclusion
The bomb should be dropped 600 m before reaching the target to ensure it hits the target.

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