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

Explanation

To solve the problem of determining the distance from the target at which the bomb should be dropped, we can follow these steps:

### Step 1: Understand the Problem
We have an airplane flying at a height of 80 meters with a horizontal velocity of 150 m/s. A bomb is dropped from the airplane and we need to find the horizontal distance from the target where the bomb should be released to ensure it hits the target.

### Step 2: Determine the Time of Fall
The first step is to calculate the time it takes for the bomb to fall from the height of 80 meters to the ground. We can use the following equation of motion:

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

Where:
- \( h = 80 \, \text{m} \) (height)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)

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

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

\[ 80 = 5 t^2 \]

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

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

### Step 3: Calculate the Horizontal Distance
Now that we have the time of fall, we can calculate the horizontal distance the bomb travels while falling. The horizontal distance \( s \) can be calculated using the formula:

\[ s = v \cdot t \]

Where:
- \( v = 150 \, \text{m/s} \) (horizontal velocity of the airplane)
- \( t = 4 \, \text{s} \) (time of fall)

Substituting the values:

\[ s = 150 \, \text{m/s} \times 4 \, \text{s} = 600 \, \text{m} \]

### Step 4: Conclusion
The bomb should be dropped 600 meters before reaching the target to ensure it hits the target.

### Final Answer
The bomb should be dropped **600 meters** from the target.

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