A bomber if flying horizontally with a constant speed of 150 m/s at a height of 78.4m. The pilot has to drop a bomb at the enemy target. AT what horizontal distance from the target shou ld be release the bomb?

Options

A. (a)0m
B. (b)300 m
C. (c)600 m
D. (d)1000 m

Answer

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

### Step 1: Determine the time of fall
The bomb is dropped from a height of 78.4 meters. We can use the equation of motion for vertical displacement to find the time it takes for the bomb to hit the ground. The equation is:

\[ S = Ut + \frac{1}{2}gt^2 \]

Where:
- \( S \) is the vertical displacement (78.4 m)
- \( U \) is the initial vertical velocity (0 m/s, since the bomb is dropped)
- \( g \) is the acceleration due to gravity (approximately 9.8 m/s², but we will take it as -9.8 m/s² for downward direction)
- \( t \) is the time in seconds

Substituting the values:

\[ -78.4 = 0 \cdot t + \frac{1}{2}(-9.8)t^2 \]

This simplifies to:

\[ -78.4 = -4.9t^2 \]

### Step 2: Solve for time \( t \)
Rearranging the equation gives:

\[ t^2 = \frac{78.4}{4.9} \]

Calculating the right side:

\[ t^2 = 16 \implies t = \sqrt{16} = 4 \text{ seconds} \]

### Step 3: Calculate the horizontal distance
Now that we have the time it takes for the bomb to fall, we can calculate the horizontal distance the bomber travels in that time. The horizontal distance \( d \) can be calculated using the formula:

\[ d = vt \]

Where:
- \( v \) is the horizontal speed of the bomber (150 m/s)
- \( t \) is the time calculated (4 seconds)

Substituting the values:

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

### Conclusion
The bomb should be released at a horizontal distance of **600 meters** from the target.

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