A bomb is dropped from an aeroplane moving horizontally at constant speed. When air resistance is taken into consideration, the bomb

Options

A. falls on the earth exactly below the aeroplane
B. falls on the earth behind the aeroplane
C. falls on the earh ahead of the aeroplane
D. flies with the aeroplane

Explanation

To solve the problem of a bomb dropped from an aeroplane moving horizontally at a constant speed while considering air resistance, we can break it down into the following steps:

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- The aeroplane is flying horizontally with a constant speed \( V_0 \).
- The bomb is dropped from the aeroplane, meaning it initially has the same horizontal velocity \( V_0 \) as the aeroplane.

2. **Vertical Motion**:
- Once the bomb is dropped, it begins to fall under the influence of gravity, with an acceleration \( g \) acting downwards.
- The initial vertical velocity of the bomb is 0 m/s.

3. **Horizontal Motion with Air Resistance**:
- In the absence of air resistance, the bomb would continue to move horizontally at speed \( V_0 \) and would land directly below the point of release.
- However, when air resistance is considered, it acts against the motion of the bomb. This resistance will reduce the horizontal velocity of the bomb as it falls.

4. **Effect of Air Resistance**:
- As the bomb falls, air resistance will cause it to decelerate in the horizontal direction.
- This means that while the aeroplane continues to move forward at speed \( V_0 \), the bomb will not maintain this speed due to the drag force acting on it.

5. **Conclusion**:
- Because of the air resistance, the bomb will land behind the aeroplane. The aeroplane moves forward while the bomb falls, resulting in the bomb landing at a point that is not directly below the aeroplane but rather behind it.

### Final Answer:
The bomb falls on the earth behind the aeroplane.

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