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

Options

A. Falls to earth exactly below the aeroplane
B. Fall to earth behind the aeroplane
C. Falls to earth ahead of the aeroplane
D. Flies with the aeroplane

Answer

To solve the problem of where the bomb will land when dropped from a horizontally moving airplane while considering air resistance, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- The airplane is moving horizontally with a constant speed \( u \).
- The bomb is dropped from the airplane, meaning it initially has the same horizontal velocity \( u \) as the airplane at the moment of release.

**Hint**: Remember that the bomb inherits the horizontal velocity of the airplane when it is dropped.

2. **Analyzing the Motion of the Bomb**:
- Once the bomb is dropped, it will start to fall vertically due to gravity while maintaining its horizontal velocity \( u \).
- In the absence of air resistance, the bomb would continue to move horizontally at speed \( u \) while falling straight down, landing directly below the point of release.

**Hint**: Consider the effects of gravity and the absence of air resistance to visualize the bomb's path.

3. **Considering Air Resistance**:
- With air resistance taken into account, the bomb will experience a drag force opposite to its direction of motion. This force will reduce its horizontal velocity over time.
- As the bomb falls, its horizontal speed will decrease due to this air resistance.

**Hint**: Think about how air resistance affects the motion of objects in free fall, particularly in the horizontal direction.

4. **Calculating the Horizontal Displacement**:
- Let \( t \) be the time it takes for the bomb to reach the ground.
- The horizontal distance traveled by the bomb can be expressed as \( vt \), where \( v \) is the horizontal velocity of the bomb at time \( t \).
- Due to air resistance, \( v < u \), meaning the bomb will not travel as far horizontally as the airplane.

**Hint**: Remember that the bomb's horizontal distance will be less than that of the airplane due to the reduction in speed caused by air resistance.

5. **Conclusion**:
- Since the airplane continues to move forward at speed \( u \) while the bomb's horizontal speed decreases, the bomb will land behind the point directly below the airplane at the moment of release.
- Therefore, the correct answer is that the bomb will fall to the earth behind the airplane.

**Hint**: Visualize the paths of both the bomb and the airplane to better understand where the bomb lands in relation to the airplane.

### Final Answer:
The bomb will fall to the earth behind the airplane.