Question

how fast would rain drops hit the ground after falling from a cloud 1 kilometer above the Earth’s surface

Answer 1

Answer on Question #62531, Physics / Mechanics | Relativity

How fast would rain drops hit the ground after falling from a cloud 1 kilometer above the Earth's surface

Solution:

Without air resistance, everything falls at the same acceleration, $9.81 \, \text{m/s/s}$. That is, every second, it goes 9.81 meters per second faster.

The speed is

$$v = \sqrt{2 g h}$$

Free fall is independent of the mass of the body. It only depends on height and time period for which body is thrown.

$$v = \sqrt{2 \cdot (9.81 \, \text{m/s}^2) \cdot (1000 \, \text{m})} = 140 \, \text{m/s}$$

Free Fall Formula is

$$y = y_0 - \frac{1}{2} g t^2$$

where $y = 0$, $y_0 = 1000 \, \text{m}$ and $g = -9.81 \, \text{m/s}^2$ is acceleration.

Thus, time of fall of the drop is

$$t = \sqrt{\frac{2 (y_0 - y)}{g}} = \sqrt{\frac{2 h}{g}} = \sqrt{\frac{2 \cdot 1000}{9.81}} \approx 14.3 \, \text{s}$$

Answer: $140 \, \text{m/s}$; $14.3 \, \text{s}$

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