Raindrops fall 1800 m from a cloud to the ground . (a) If they were not slowed by air resistance, how fast would the drops be moving when they struck the ground ? (b) Would it be safe to walk outside during a rainstorm ?

Answer

To solve the problem step by step, we will address both parts of the question regarding the raindrops falling from a height of 1800 meters.

### Part (a): Speed of Raindrops When They Strike the Ground

1. **Identify Given Data**:
- Height (s) = 1800 m (downward, so we will consider it as -1800 m)
- Initial velocity (u) = 0 m/s (the raindrops start from rest)
- Acceleration due to gravity (a) = -9.8 m/s² (downward)

2. **Use the Kinematic Equation**:
We will use the kinematic equation:
\[ v^2 = u^2 + 2as \]
where:
- \( v \) = final velocity
- \( u \) = initial velocity
- \( a \) = acceleration
- \( s \) = displacement

3. **Substitute the Values**:
Substituting the known values into the equation:
\[ v^2 = 0^2 + 2 \times (-9.8) \times (-1800) \]
\[ v^2 = 0 + 2 \times 9.8 \times 1800 \]
\[ v^2 = 35280 \]

4. **Calculate Final Velocity**:
Now, take the square root to find \( v \):
\[ v = \sqrt{35280} \approx 187.8 \text{ m/s} \]

5. **Interpret the Result**:
The speed of the raindrops when they strike the ground would be approximately 187.8 m/s.

### Part (b): Safety of Walking Outside During a Rainstorm

1. **Evaluate the Speed**:
The calculated speed of the raindrops (187.8 m/s) is very high. For comparison, the speed of a bullet is around 200 m/s.

2. **Conclusion**:
Given that the raindrops would be falling at a speed comparable to that of a bullet, it would not be safe to walk outside during a rainstorm, as being struck by a raindrop at this speed could cause serious injury.

### Final Answers:
- (a) The speed of the raindrops when they strike the ground is approximately 187.8 m/s.
- (b) It is not safe to walk outside during a rainstorm.