Wind is blowing in the north direction at speed of 2 m/s which causes the rain to fall at some angle with the vertical. With what velocity should acyclist drive so that the rain appears vertical to him:

Options

A. 2 m/s south
B. 2 m/s north
C. 4 m/s west
D. 4 m/s south

Answer

To solve the problem, we need to determine the speed at which a cyclist should travel so that the rain appears to fall vertically to him, given that the wind is blowing in the north direction at a speed of 2 m/s.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- The wind is blowing north at a speed of 2 m/s.
- Rain falls at an angle due to this wind. We need to find the speed of the cyclist so that the rain appears to fall straight down.

2. **Setting Up the Coordinate System**:
- Let's define our coordinate system:
- North direction as positive y-axis.
- East direction as positive x-axis.
- Downward direction (due to gravity) as negative z-axis.

3. **Velocity of Rain**:
- The velocity of the rain can be represented as a vector.
- Let \( v_r \) be the velocity of the rain.
- Since the rain falls vertically downwards due to gravity, we can express the velocity of the rain as:
\[ v_r = v_{1} \hat{j} - v_{2} \hat{i} \]
where \( v_{1} \) is the downward velocity of the rain and \( v_{2} = 2 \, \text{m/s} \) is the horizontal velocity due to the wind.

4. **Velocity of the Cyclist**:
- Let \( v_c \) be the velocity of the cyclist.
- The cyclist needs to travel in the south direction to counteract the northward wind. Therefore, we can express the cyclist's velocity as:
\[ v_c = -v_c \hat{i} \]

5. **Relative Velocity Condition**:
- For the rain to appear vertical to the cyclist, the horizontal component of the rain's velocity relative to the cyclist must be zero.
- This means:
\[ v_c + v_{2} = 0 \]
- Substituting \( v_{2} = 2 \, \text{m/s} \):
\[ v_c + 2 = 0 \]

6. **Solving for Cyclist's Velocity**:
- Rearranging the equation gives:
\[ v_c = -2 \, \text{m/s} \]
- This indicates that the cyclist must travel at a speed of 2 m/s in the south direction (since we defined south as negative x-direction).

7. **Conclusion**:
- The cyclist should drive at a speed of 2 m/s towards the south so that the rain appears to fall vertically to him.

### Final Answer:
The cyclist should drive at a speed of **2 m/s towards the south**.