Water drips from rest from a leaf that is 20 meters above the ground. Neglecting air resistance, what is the speed of each water drop when it hits the ground ?

Options

A. 30 m/s
B. 40 m/s
C. 20 m/s
D. 15 m/s

Answer

To solve the problem of determining the speed of each water drop when it hits the ground, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Height (h) = 20 meters
- Initial velocity (u) = 0 m/s (since the water drops from rest)
- Acceleration due to gravity (g) = 10 m/s² (approximated for simplicity)

2. **Choose a Reference Point**:
- We will consider the downward direction as positive for this problem.

3. **Use the Appropriate Equation of Motion**:
- We can use the third equation of motion, which relates initial velocity, final velocity, acceleration, and displacement:
\[ v^2 = u^2 + 2as \]
- Here, \( v \) is the final velocity, \( u \) is the initial velocity, \( a \) is the acceleration, and \( s \) is the displacement.

4. **Substitute the Known Values**:
- In our case:
- \( u = 0 \) m/s (initial velocity)
- \( a = g = 10 \) m/s² (acceleration due to gravity)
- \( s = h = 20 \) m (displacement)
- Plugging these values into the equation:
\[ v^2 = 0^2 + 2 \times 10 \times 20 \]
\[ v^2 = 0 + 400 \]
\[ v^2 = 400 \]

5. **Calculate the Final Velocity**:
- To find \( v \), take the square root of both sides:
\[ v = \sqrt{400} = 20 \text{ m/s} \]

6. **Conclusion**:
- The speed of each water drop when it hits the ground is **20 m/s**.